/*
 *  This library is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU Lesser General Public
 *  License as published by the Free Software Foundation; either
 *  version 2 of the License, or (at your option) any later version.
 *
 *  This library is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *  Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 * 
 *  Some functions in this file use the VSOP87 solution by
 *  Messrs. Bretagnon and Francou.
 * 
 *  Copyright (C) 2000 - 2005 Liam Girdwood  
 */

#include <math.h>
#include <libnova/jupiter.h>
#include <libnova/vsop87.h>
#include <libnova/solar.h>
#include <libnova/earth.h>
#include <libnova/transform.h>
#include <libnova/rise_set.h>
#include <libnova/utility.h>

#define LONG_L0 860
#define LONG_L1 426
#define LONG_L2 225
#define LONG_L3 120
#define LONG_L4 48
#define LONG_L5 11
#define LAT_B0 249
#define LAT_B1 120
#define LAT_B2 82
#define LAT_B3 33
#define LAT_B4 13
#define LAT_B5 3
#define RADIUS_R0 727
#define RADIUS_R1 371
#define RADIUS_R2 186
#define RADIUS_R3 97
#define RADIUS_R4 45
#define RADIUS_R5 9

/* cache variables */
static double cJD = 0, cL = 0, cB = 0, cR = 0;

static const struct ln_vsop jupiter_longitude_l0[LONG_L0] = {
    {     0.59954691494,  0.00000000000,        0.00000000000}, 
    {     0.09695898719,  5.06191793158,      529.69096509460}, 
    {     0.00573610142,  1.44406205629,        7.11354700080}, 
    {     0.00306389205,  5.41734730184,     1059.38193018920}, 
    {     0.00097178296,  4.14264726552,      632.78373931320}, 
    {     0.00072903078,  3.64042916389,      522.57741809380}, 
    {     0.00064263975,  3.41145165351,      103.09277421860}, 
    {     0.00039806064,  2.29376740788,      419.48464387520}, 
    {     0.00038857767,  1.27231755835,      316.39186965660}, 
    {     0.00027964629,  1.78454591820,      536.80451209540}, 
    {     0.00013589730,  5.77481040790,     1589.07289528380}, 
    {     0.00008246349,  3.58227925840,      206.18554843720}, 
    {     0.00008768704,  3.63000308199,      949.17560896980}, 
    {     0.00007368042,  5.08101194270,      735.87651353180}, 
    {     0.00006263150,  0.02497628807,      213.29909543800}, 
    {     0.00006114062,  4.51319998626,     1162.47470440780}, 
    {     0.00004905396,  1.32084470588,      110.20632121940}, 
    {     0.00005305285,  1.30671216791,       14.22709400160}, 
    {     0.00005305441,  4.18625634012,     1052.26838318840}, 
    {     0.00004647248,  4.69958103684,        3.93215326310}, 
    {     0.00003045023,  4.31676431084,      426.59819087600}, 
    {     0.00002609999,  1.56667394063,      846.08283475120}, 
    {     0.00002028191,  1.06376530715,        3.18139373770}, 
    {     0.00001764763,  2.14148655117,     1066.49547719000}, 
    {     0.00001722972,  3.88036268267,     1265.56747862640}, 
    {     0.00001920945,  0.97168196472,      639.89728631400}, 
    {     0.00001633223,  3.58201833555,      515.46387109300}, 
    {     0.00001431999,  4.29685556046,      625.67019231240}, 
    {     0.00000973272,  4.09764549134,       95.97922721780}, 
    {     0.00000884457,  2.43700227469,      412.37109687440}, 
    {     0.00000732853,  6.08535124451,      838.96928775040}, 
    {     0.00000731094,  3.80592308125,     1581.95934828300}, 
    {     0.00000691971,  6.13365277914,     2118.76386037840}, 
    {     0.00000709166,  1.29274760330,      742.99006053260}, 
    {     0.00000614482,  4.10850580886,     1478.86657406440}, 
    {     0.00000495219,  3.75564106217,      323.50541665740}, 
    {     0.00000581903,  4.53969579398,      309.27832265580}, 
    {     0.00000375664,  4.70304250208,     1368.66025284500}, 
    {     0.00000389876,  4.89706786539,     1692.16566950240}, 
    {     0.00000341016,  5.71452379310,      533.62311835770}, 
    {     0.00000330458,  4.74049819491,        0.04818410980}, 
    {     0.00000440853,  2.95818598959,      454.90936652730}, 
    {     0.00000417267,  1.03554397138,        2.44768055480}, 
    {     0.00000244174,  5.22024286247,      728.76296653100}, 
    {     0.00000261541,  1.87652515753,        0.96320784650}, 
    {     0.00000256589,  3.72410394286,      199.07200143640}, 
    {     0.00000261005,  0.82048379203,      380.12776796000}, 
    {     0.00000220381,  1.65114584814,      543.91805909620}, 
    {     0.00000201991,  1.80692992449,     1375.77379984580}, 
    {     0.00000207336,  1.85463683689,      525.75881183150}, 
    {     0.00000197061,  5.29255821015,     1155.36115740700}, 
    {     0.00000235139,  1.22694468346,      909.81873305460}, 
    {     0.00000174827,  5.90974976879,      956.28915597060}, 
    {     0.00000149385,  4.37744775359,     1685.05212250160}, 
    {     0.00000175197,  3.22647697998,     1898.35121793960}, 
    {     0.00000175172,  3.72977441220,      942.06206196900}, 
    {     0.00000157917,  4.36478445901,     1795.25844372100}, 
    {     0.00000137898,  1.31800455202,     1169.58825140860}, 
    {     0.00000117498,  2.50021486074,     1596.18644228460}, 
    {     0.00000150504,  3.90624455135,       74.78159856730}, 
    {     0.00000116786,  3.38920921060,        0.52126486180}, 
    {     0.00000105894,  4.55439354032,      526.50957135690}, 
    {     0.00000130540,  4.16876671917,     1045.15483618760}, 
    {     0.00000141388,  3.13579930728,      491.55792945680}, 
    {     0.00000099524,  1.42112622270,      532.87235883230}, 
    {     0.00000096143,  1.18143253105,      117.31986822020}, 
    {     0.00000091732,  0.85722451006,     1272.68102562720}, 
    {     0.00000087704,  1.21730504350,      453.42489381900}, 
    {     0.00000068531,  2.35201905890,        2.92076130680}, 
    {     0.00000066111,  5.34380967040,     1471.75302706360}, 
    {     0.00000077401,  4.42676354183,       39.35687591520}, 
    {     0.00000072028,  4.23856425835,     2111.65031337760}, 
    {     0.00000063345,  4.97658360088,        0.75075952540}, 
    {     0.00000059423,  4.11122034593,     2001.44399215820}, 
    {     0.00000062471,  0.51213142347,      220.41264243880}, 
    {     0.00000066540,  2.98844410276,     2214.74308759620}, 
    {     0.00000060295,  4.12633619420,        4.19278569400}, 
    {     0.00000056014,  1.15477785231,       21.34064100240}, 
    {     0.00000052954,  0.91283039851,       10.29494073850}, 
    {     0.00000070461,  5.14178006023,      835.03713448730}, 
    {     0.00000051903,  4.10065404719,     1258.45393162560}, 
    {     0.00000046583,  4.66599487054,        5.62907429250}, 
    {     0.00000058261,  5.86719898935,     5753.38488489680}, 
    {     0.00000040103,  4.68801114087,        0.16005869440}, 
    {     0.00000046785,  4.79414027278,      305.34616939270}, 
    {     0.00000039306,  4.25499338010,      853.19638175200}, 
    {     0.00000046153,  5.10982849847,        4.66586644600}, 
    {     0.00000054583,  1.57071663540,      983.11585891360}, 
    {     0.00000038921,  6.07598407822,      518.64526483070}, 
    {     0.00000038460,  2.43832240008,      433.71173787680}, 
    {     0.00000046910,  3.54638837922,        5.41662597140}, 
    {     0.00000041834,  4.67980756775,      302.16477565500}, 
    {     0.00000035921,  2.45088327353,      430.53034413910}, 
    {     0.00000039307,  1.71678059616,       11.04570026390}, 
    {     0.00000037895,  0.21140086073,     2648.45482547300}, 
    {     0.00000037566,  6.19479786035,      831.85574074960}, 
    {     0.00000035845,  4.61505536309,     2008.55753915900}, 
    {     0.00000043402,  0.14992219581,      528.20649238630}, 
    {     0.00000031581,  5.14178165108,     1788.14489672020}, 
    {     0.00000029860,  5.34424466576,     2221.85663459700}, 
    {     0.00000032959,  5.28952640380,       88.86568021700}, 
    {     0.00000027686,  1.85227036207,        0.21244832110}, 
    {     0.00000025821,  3.85920335036,     2317.83586181480}, 
    {     0.00000024705,  2.63498818000,      114.13847448250}, 
    {     0.00000033844,  1.00563073311,     9683.59458111640}, 
    {     0.00000024248,  3.82564321484,     1574.84580128220}, 
    {     0.00000027111,  2.80845416546,       18.15924726470}, 
    {     0.00000026837,  1.77586073782,      532.13864564940}, 
    {     0.00000026212,  2.74456887801,     2531.13495725280}, 
    {     0.00000030765,  0.42330199069,        1.48447270830}, 
    {     0.00000030469,  3.66675723074,      508.35032409220}, 
    {     0.00000023191,  3.24511984498,      984.60033162190}, 
    {     0.00000019445,  0.52370214464,       14.97785352700}, 
    {     0.00000019331,  4.85656303715,     1361.54670584420}, 
    {     0.00000022889,  3.85009333532,     2428.04218303420}, 
    {     0.00000021613,  6.01647014213,     1063.31408345230}, 
    {     0.00000020167,  5.59590496803,      527.24328453980}, 
    {     0.00000023732,  2.52764898478,      494.26624244250}, 
    {     0.00000020190,  1.01559114881,      628.85158605010}, 
    {     0.00000015994,  5.09003506053,      529.73914920440}, 
    {     0.00000016134,  5.27096450385,      142.44965013380}, 
    {     0.00000020697,  4.03443555572,      355.74874557180}, 
    {     0.00000021480,  1.28666873894,       35.42472265210}, 
    {     0.00000014981,  4.86119818170,     2104.53676637680}, 
    {     0.00000017242,  1.59187221366,     1439.50969814920}, 
    {     0.00000015994,  1.89222393849,      529.64278098480}, 
    {     0.00000017957,  4.30177741048,        6.15033915430}, 
    {     0.00000013287,  2.18960688770,     1055.44977692610}, 
    {     0.00000014809,  0.87727524457,       99.16062095550}, 
    {     0.00000014148,  2.71597731671,        0.26063243090}, 
    {     0.00000014202,  2.41335744746,      530.65417294110}, 
    {     0.00000015331,  6.07685758999,      149.56319713460}, 
    {     0.00000015832,  4.11682340572,      636.71589257630}, 
    {     0.00000016199,  2.77035135003,      760.25553592000}, 
    {     0.00000012258,  2.61067822838,      405.25754987360}, 
    {     0.00000013665,  3.56042954023,      217.23124870110}, 
    {     0.00000015261,  2.81823022031,      621.73803904930}, 
    {     0.00000014680,  6.26419083616,      569.04784100980}, 
    {     0.00000012529,  1.39076773846,        7.06536289100}, 
    {     0.00000011603,  4.60461324892,        7.16173111060}, 
    {     0.00000011676,  3.60450719576,     2634.22773147140}, 
    {     0.00000012182,  0.24373178668,     1485.98012106520}, 
    {     0.00000011352,  2.00814398370,     1073.60902419080}, 
    {     0.00000011241,  2.48010676188,      423.41679713830}, 
    {     0.00000010942,  5.03605236981,      458.84151979040}, 
    {     0.00000011121,  4.04930841517,      519.39602435610}, 
    {     0.00000012266,  4.30151937187,      604.47256366190}, 
    {     0.00000013150,  2.72184449861,     1364.72809958190}, 
    {     0.00000010604,  3.11518747071,        1.27202438720}, 
    {     0.00000009873,  1.70233190646,     1699.27921650320}, 
    {     0.00000010828,  5.08717082517,     2324.94940881560}, 
    {     0.00000010692,  2.51399278354,     2847.52682690940}, 
    {     0.00000012646,  4.75590815200,      528.72775724810}, 
    {     0.00000010084,  4.05599680401,       38.13303563780}, 
    {     0.00000011536,  2.35035142816,      643.82943957710}, 
    {     0.00000010218,  3.65818193440,      107.02492748170}, 
    {     0.00000010234,  3.63741793836,     2744.43405269080}, 
    {     0.00000010105,  1.31344662885,     1905.46476494040}, 
    {     0.00000009338,  5.92214604272,     1148.24761040620}, 
    {     0.00000008796,  2.77421597882,        6.59228213900}, 
    {     0.00000008421,  4.52526352162,     1677.93857550080}, 
    {     0.00000010128,  2.09031029378,      511.53171782990}, 
    {     0.00000008280,  2.98793394775,      540.73666535850}, 
    {     0.00000009753,  1.22443091754,       32.24332891440}, 
    {     0.00000010629,  2.07778578633,       92.04707395470}, 
    {     0.00000007886,  0.99641706679,      408.43894361130}, 
    {     0.00000008813,  3.46912264870,     1021.24889455140}, 
    {     0.00000007941,  2.86765260965,     2125.87740737920}, 
    {     0.00000008575,  5.29585347114,      415.55249061210}, 
    {     0.00000007841,  6.08025868276,       70.84944530420}, 
    {     0.00000007706,  1.69807427167,        8.07675484730}, 
    {     0.00000007265,  4.65479123794,      629.60234557550}, 
    {     0.00000007163,  4.93237560809,     1056.20053645150}, 
    {     0.00000007248,  4.61590472787,     2420.92863603340}, 
    {     0.00000007712,  2.13818572880,       33.94024994380}, 
    {     0.00000006645,  0.45640663795,      635.96513305090}, 
    {     0.00000009377,  4.03158387581,     2810.92146160520}, 
    {     0.00000008221,  1.23649767817,     1802.37199072180}, 
    {     0.00000006340,  0.07280718454,      202.25339517410}, 
    {     0.00000006383,  3.54298789012,     1891.23767093880}, 
    {     0.00000007901,  2.32514375888,      230.56457082540}, 
    {     0.00000006214,  4.54560345236,        2.70831298570}, 
    {     0.00000007347,  1.24457591968,       24.37902238820}, 
    {     0.00000007472,  3.02787419533,      330.61896365820}, 
    {     0.00000006246,  1.77826735859,     1062.56332392690}, 
    {     0.00000005674,  5.14130380414,      746.92221379570}, 
    {     0.00000005855,  5.42127169330,       28.31117565130}, 
    {     0.00000005629,  3.24347319369,      529.16970023280}, 
    {     0.00000007653,  0.52812977555,      672.14061522840}, 
    {     0.00000005456,  3.34715399006,     2950.61960112800}, 
    {     0.00000007127,  1.43485695449,        6.21977512350}, 
    {     0.00000005388,  4.90171438369,       69.15252427480}, 
    {     0.00000005608,  4.98112575538,     2641.34127847220}, 
    {     0.00000005843,  2.95362326688,      490.33408917940}, 
    {     0.00000004943,  5.37603229206,      721.64941953020}, 
    {     0.00000005120,  4.85758375369,       31.01948863700}, 
    {     0.00000005163,  5.07430434384,       67.66805156650}, 
    {     0.00000004738,  6.10247687172,      106.27416795630}, 
    {     0.00000004879,  0.07093292758,       78.71375183040}, 
    {     0.00000004854,  5.63875710470,        1.69692102940}, 
    {     0.00000005629,  3.73870719507,      530.21222995640}, 
    {     0.00000004471,  4.49152590899,      505.31194270640}, 
    {     0.00000004313,  4.79367774897,      535.10759106600}, 
    {     0.00000004280,  0.54783823710,        1.43628859850}, 
    {     0.00000004453,  0.50550043817,      524.06189080210}, 
    {     0.00000004936,  4.82992128024,      422.66603761290}, 
    {     0.00000004701,  3.41632316320,     3060.82592234740}, 
    {     0.00000004261,  2.67050830494,      561.93429400900}, 
    {     0.00000004156,  4.00674305729,       99.91138048090}, 
    {     0.00000004561,  2.29662333497,     3163.91869656600}, 
    {     0.00000004414,  5.67223937661,     1464.63948006280}, 
    {     0.00000005270,  3.89098773035,      191.95845443560}, 
    {     0.00000005344,  0.31505537960,     1289.94650101460}, 
    {     0.00000003856,  4.28927088609,     1994.33044515740}, 
    {     0.00000004227,  5.32680781419,     2538.24850425360}, 
    {     0.00000003968,  4.56799284427,     1382.88734684660}, 
    {     0.00000003874,  1.56573094048,      647.01083331480}, 
    {     0.00000004227,  5.51697565211,     5223.69391980220}, 
    {     0.00000004130,  2.81118299519,      416.30325013750}, 
    {     0.00000003662,  4.35201972236,     2737.32050569000}, 
    {     0.00000003584,  5.48543989133,      750.10360753340}, 
    {     0.00000004329,  0.84948546685,      531.17543780290}, 
    {     0.00000004093,  0.19987691246,      525.02509864860}, 
    {     0.00000003400,  6.00302355875,        1.22384027740}, 
    {     0.00000003496,  0.31250621097,      597.35901666110}, 
    {     0.00000003957,  1.92811865595,     1512.80682400820}, 
    {     0.00000003299,  4.27641782638,      526.77020378780}, 
    {     0.00000003218,  2.90660065796,      963.40270297140}, 
    {     0.00000003150,  3.81062282472,      280.96714700450}, 
    {     0.00000004129,  4.74946631331,        0.89377187730}, 
    {     0.00000003840,  1.91064921809,      378.64329525170}, 
    {     0.00000003057,  1.65588839054,      528.94020556920}, 
    {     0.00000003011,  1.59274545702,      224.34479570190}, 
    {     0.00000003197,  5.86630896662,        4.14460158420}, 
    {     0.00000003628,  0.07910101827,      558.00214074590}, 
    {     0.00000002932,  0.41424504523,        7.86430652620}, 
    {     0.00000003316,  2.70210829186,      532.61172640140}, 
    {     0.00000002925,  4.47579366684,      533.88375078860}, 
    {     0.00000003688,  0.39899953746,      685.47393735270}, 
    {     0.00000003224,  2.45813595822,      960.22130923370}, 
    {     0.00000003059,  5.32615258179,      530.44172462000}, 
    {     0.00000003383,  4.42166889790,      312.45971639350}, 
    {     0.00000003321,  2.71397444568,      495.75071515080}, 
    {     0.00000002698,  5.23121581439,      739.80866679490}, 
    {     0.00000003591,  2.30995707520,      908.33426034630}, 
    {     0.00000002619,  3.09144103989,     3267.01147078460}, 
    {     0.00000003567,  5.07207593227,       73.29712585900}, 
    {     0.00000002797,  2.98948711408,      483.22054217860}, 
    {     0.00000003397,  3.29611266379,      911.30320576290}, 
    {     0.00000003352,  1.44371985824,      593.42686339800}, 
    {     0.00000002563,  3.35095990562,     2207.62954059540}, 
    {     0.00000002553,  0.36858603419,     1048.33622992530}, 
    {     0.00000002621,  3.82783663712,      520.12973753900}, 
    {     0.00000003356,  1.08298579333,       46.47042291600}, 
    {     0.00000003397,  3.83080921477,      210.11770170030}, 
    {     0.00000003023,  5.52874613382,      618.55664531160}, 
    {     0.00000002498,  0.47888741754,      945.24345570670}, 
    {     0.00000002665,  0.49714213041,     1057.89745748090}, 
    {     0.00000002322,  5.87923753103,     2751.54759969160}, 
    {     0.00000002587,  0.03759881914,        1.64453140270}, 
    {     0.00000002901,  2.50012990691,      525.49817940060}, 
    {     0.00000003153,  2.30879679988,      457.61767951300}, 
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    {     0.00000000099,  4.22263740110,     8521.11987670860}, 
    {     0.00000000078,  5.75868229769,     5812.37352203900}, 
    {     0.00000000078,  4.55958930291,     4752.99159184980}, 
    {     0.00000000080,  1.07708178317,     5378.66178416220}, 
    {     0.00000000078,  0.76677000831,      525.54636351040}, 
    {     0.00000000081,  3.10720885599,     2527.20280398970}, 
    {     0.00000000081,  0.45113135705,     2516.90786325120}, 
    {     0.00000000098,  1.42656513937,      757.21715453420}, 
    {     0.00000000087,  4.62233814403,      184.98791978670}, 
    {     0.00000000103,  2.56729943579,     1124.34166877000}, 
    {     0.00000000102,  1.33070990614,     3782.47534187760}, 
    {     0.00000000084,  5.05086451175,     1160.02702385300}, 
    {     0.00000000079,  2.29616426691,     2758.66114669240}, 
    {     0.00000000080,  0.85136002390,     1791.32629045790}, 
    {     0.00000000075,  5.42366672204,     2755.47975295470}, 
    {     0.00000000085,  1.86831566677,    25028.52121138500}, 
    {     0.00000000079,  4.70716888788,     4120.20785253660}, 
    {     0.00000000073,  4.69119414591,     2115.58246664070}, 
    {     0.00000000098,  3.93222636960,     2124.98363550190}, 
    {     0.00000000072,  3.82048491843,     4539.69249641180}, 
    {     0.00000000081,  5.76205552882,      617.80588578620}, 
};


static const struct ln_vsop jupiter_longitude_l1[LONG_L1] = {
    {   529.69096508814,  0.00000000000,        0.00000000000}, 
    {     0.00489503243,  4.22082939470,      529.69096509460}, 
    {     0.00228917222,  6.02646855621,        7.11354700080}, 
    {     0.00030099479,  4.54540782858,     1059.38193018920}, 
    {     0.00020720920,  5.45943156902,      522.57741809380}, 
    {     0.00012103653,  0.16994816098,      536.80451209540}, 
    {     0.00006067987,  4.42422292017,      103.09277421860}, 
    {     0.00005433968,  3.98480737746,      419.48464387520}, 
    {     0.00004237744,  5.89008707199,       14.22709400160}, 
    {     0.00002211974,  5.26766687382,      206.18554843720}, 
    {     0.00001983502,  4.88600705699,     1589.07289528380}, 
    {     0.00001295769,  5.55132752171,        3.18139373770}, 
    {     0.00001163416,  0.51450634873,        3.93215326310}, 
    {     0.00001007167,  0.46474690033,      735.87651353180}, 
    {     0.00001174094,  5.84238857133,     1052.26838318840}, 
    {     0.00000847762,  5.75765726863,      110.20632121940}, 
    {     0.00000827250,  4.80311857692,      213.29909543800}, 
    {     0.00000829822,  0.59345481695,     1066.49547719000}, 
    {     0.00001003864,  3.14841622246,      426.59819087600}, 
    {     0.00001098730,  5.30705242117,      515.46387109300}, 
    {     0.00000724923,  5.51690038433,      639.89728631400}, 
    {     0.00000567826,  5.98865760444,      625.67019231240}, 
    {     0.00000474197,  4.13243716360,      412.37109687440}, 
    {     0.00000412936,  5.73653788228,       95.97922721780}, 
    {     0.00000336820,  3.72892266066,     1162.47470440780}, 
    {     0.00000345412,  4.24128387922,      632.78373931320}, 
    {     0.00000234071,  6.24295755869,      309.27832265580}, 
    {     0.00000194827,  2.21824346028,      323.50541665740}, 
    {     0.00000234805,  4.03315571261,      949.17560896980}, 
    {     0.00000183904,  6.27973919510,      543.91805909620}, 
    {     0.00000198512,  1.50446971008,      838.96928775040}, 
    {     0.00000186807,  6.07956275814,      742.99006053260}, 
    {     0.00000171405,  5.41658811525,      199.07200143640}, 
    {     0.00000130777,  0.62641588161,      728.76296653100}, 
    {     0.00000134095,  5.23702273624,     2118.76386037840}, 
    {     0.00000115444,  0.67783747230,      846.08283475120}, 
    {     0.00000106501,  4.47671724240,      956.28915597060}, 
    {     0.00000066832,  5.73362353275,       21.34064100240}, 
    {     0.00000069619,  5.97256378090,      532.87235883230}, 
    {     0.00000059950,  1.00657473790,     1596.18644228460}, 
    {     0.00000063366,  6.05635396519,     1581.95934828300}, 
    {     0.00000079718,  5.82156733700,     1045.15483618760}, 
    {     0.00000065635,  0.12938321631,      526.50957135690}, 
    {     0.00000058519,  0.58687309667,     1155.36115740700}, 
    {     0.00000056610,  1.41183572003,      533.62311835770}, 
    {     0.00000071631,  5.34149334443,      942.06206196900}, 
    {     0.00000057343,  5.96870336620,     1169.58825140860}, 
    {     0.00000055048,  5.42871116938,       10.29494073850}, 
    {     0.00000052026,  0.22999191591,     1368.66025284500}, 
    {     0.00000052295,  5.72636754267,      117.31986822020}, 
    {     0.00000050427,  6.08258832558,      525.75881183150}, 
    {     0.00000047278,  3.60428393787,     1478.86657406440}, 
    {     0.00000042199,  4.13113112919,     1692.16566950240}, 
    {     0.00000046566,  0.51168261375,     1265.56747862640}, 
    {     0.00000032801,  5.03520269183,      220.41264243880}, 
    {     0.00000033556,  0.09960615979,      302.16477565500}, 
    {     0.00000029379,  3.35927110207,        4.66586644600}, 
    {     0.00000029311,  0.75894050642,       88.86568021700}, 
    {     0.00000032449,  5.37487176787,      508.35032409220}, 
    {     0.00000029741,  5.42345191096,     1272.68102562720}, 
    {     0.00000021789,  6.14949766217,     1685.05212250160}, 
    {     0.00000025194,  1.60716361937,      831.85574074960}, 
    {     0.00000021133,  5.86310776376,     1258.45393162560}, 
    {     0.00000019668,  2.18904500387,      316.39186965660}, 
    {     0.00000017878,  0.82813691085,      433.71173787680}, 
    {     0.00000017409,  2.75647882058,      853.19638175200}, 
    {     0.00000017703,  5.95527033658,        5.41662597140}, 
    {     0.00000018586,  0.51459954175,     1375.77379984580}, 
    {     0.00000017469,  0.70855164060,     1471.75302706360}, 
    {     0.00000014369,  0.91459684737,       18.15924726470}, 
    {     0.00000014107,  0.63031131929,        2.92076130680}, 
    {     0.00000011728,  1.76421689491,      380.12776796000}, 
    {     0.00000011042,  5.56386292919,     1574.84580128220}, 
    {     0.00000011422,  4.30273286555,      405.25754987360}, 
    {     0.00000010407,  0.30595619562,     1361.54670584420}, 
    {     0.00000009894,  0.38972478935,     1073.60902419080}, 
    {     0.00000009808,  5.90342059427,      519.39602435610}, 
    {     0.00000009287,  3.23717178839,     1795.25844372100}, 
    {     0.00000009079,  5.59391515894,     2648.45482547300}, 
    {     0.00000008830,  0.53669085248,     1788.14489672020}, 
    {     0.00000008238,  5.88621877345,     2001.44399215820}, 
    {     0.00000008058,  5.07394631539,     1485.98012106520}, 
    {     0.00000006690,  2.41093500491,        4.19278569400}, 
    {     0.00000005917,  4.17942020818,     2008.55753915900}, 
    {     0.00000007256,  6.19390446816,       11.04570026390}, 
    {     0.00000006272,  1.36131578474,     1148.24761040620}, 
    {     0.00000005142,  5.23124680535,      628.85158605010}, 
    {     0.00000005141,  2.92956226336,      518.64526483070}, 
    {     0.00000004764,  0.16833299921,      629.60234557550}, 
    {     0.00000004603,  0.78535347104,      721.64941953020}, 
    {     0.00000004573,  6.24771751154,     1677.93857550080}, 
    {     0.00000004536,  4.95109388690,      635.96513305090}, 
    {     0.00000004434,  1.45220762308,     2125.87740737920}, 
    {     0.00000004518,  2.06522259381,      453.42489381900}, 
    {     0.00000004428,  0.15677546362,     1699.27921650320}, 
    {     0.00000005594,  5.57471241370,      191.95845443560}, 
    {     0.00000005405,  1.46221153779,      330.61896365820}, 
    {     0.00000005776,  4.37575545399,     2221.85663459700}, 
    {     0.00000004265,  0.24198200812,     2104.53676637680}, 
    {     0.00000004100,  6.19338226411,      636.71589257630}, 
    {     0.00000004432,  4.35787390405,      423.41679713830}, 
    {     0.00000004102,  0.49195461480,     1056.20053645150}, 
    {     0.00000004527,  0.09244775677,     1062.56332392690}, 
    {     0.00000004397,  4.14273244974,      511.53171782990}, 
    {     0.00000003567,  5.66550104255,     2317.83586181480}, 
    {     0.00000003585,  0.28040162482,     1055.44977692610}, 
    {     0.00000004009,  2.54842404074,       74.78159856730}, 
    {     0.00000003686,  2.93367849990,       32.24332891440}, 
    {     0.00000002969,  5.50022776972,      107.02492748170}, 
    {     0.00000002856,  5.73809418496,       99.91138048090}, 
    {     0.00000002718,  1.25246874516,      540.73666535850}, 
    {     0.00000002808,  3.30714906571,        0.75075952540}, 
    {     0.00000002669,  1.63398531390,     1063.31408345230}, 
    {     0.00000002667,  4.28683044077,      106.27416795630}, 
    {     0.00000002705,  3.03568370231,      422.66603761290}, 
    {     0.00000003271,  5.89438924876,     1802.37199072180}, 
    {     0.00000002654,  0.35475530647,     1898.35121793960}, 
    {     0.00000002574,  3.59809745049,      750.10360753340}, 
    {     0.00000002486,  5.28928577587,     1891.23767093880}, 
    {     0.00000003221,  4.58424996327,      416.30325013750}, 
    {     0.00000002936,  1.09054035208,     1464.63948006280}, 
    {     0.00000002398,  6.02106328658,      551.03160609700}, 
    {     0.00000002214,  5.24451644028,      621.73803904930}, 
    {     0.00000002193,  0.00364881833,     2420.92863603340}, 
    {     0.00000002320,  5.82908812407,      305.34616939270}, 
    {     0.00000002088,  5.99245749935,     1994.33044515740}, 
    {     0.00000002042,  0.75011275470,      142.44965013380}, 
    {     0.00000002021,  4.17581114855,      569.04784100980}, 
    {     0.00000002110,  6.25440423633,      647.01083331480}, 
    {     0.00000002110,  5.18650189729,      227.52618943960}, 
    {     0.00000002279,  5.79998105466,      539.98590583310}, 
    {     0.00000002004,  4.20934218728,     2324.94940881560}, 
    {     0.00000001977,  3.99196981525,       24.37902238820}, 
    {     0.00000001953,  1.35695450633,      963.40270297140}, 
    {     0.00000001896,  2.78687918909,     2428.04218303420}, 
    {     0.00000001970,  5.88674791355,      217.23124870110}, 
    {     0.00000001931,  3.03273886284,     1382.88734684660}, 
    {     0.00000002034,  3.08513086760,      408.43894361130}, 
    {     0.00000001833,  5.61442879983,      430.53034413910}, 
    {     0.00000001838,  1.25469566267,       81.75213321620}, 
    {     0.00000001820,  5.97506520830,      114.13847448250}, 
    {     0.00000002043,  4.34071262566,       70.84944530420}, 
    {     0.00000001957,  4.03064578017,       92.04707395470}, 
    {     0.00000001768,  0.33096757704,       35.42472265210}, 
    {     0.00000002328,  5.86166964748,     1038.04128918680}, 
    {     0.00000001831,  4.81134529978,      124.43341522100}, 
    {     0.00000002268,  1.02652901220,      618.55664531160}, 
    {     0.00000001919,  5.01339713289,       99.16062095550}, 
    {     0.00000001923,  0.28688541174,       31.01948863700}, 
    {     0.00000002359,  4.65803416282,     1905.46476494040}, 
    {     0.00000001879,  5.69252482087,      210.11770170030}, 
    {     0.00000001678,  0.25561675979,      295.05122865420}, 
    {     0.00000001656,  5.46017983557,     2634.22773147140}, 
    {     0.00000001675,  6.15616456038,      643.82943957710}, 
    {     0.00000001953,  5.09846435548,       17.40848773930}, 
    {     0.00000001539,  2.75248075364,      415.55249061210}, 
    {     0.00000001482,  3.76735041917,      534.35683154060}, 
    {     0.00000001446,  3.15802770791,       25.12978191360}, 
    {     0.00000001421,  0.61909506285,      458.84151979040}, 
    {     0.00000001666,  0.26032169128,      835.03713448730}, 
    {     0.00000001472,  0.83054329617,       28.31117565130}, 
    {     0.00000001654,  0.88874938135,     1781.03134971940}, 
    {     0.00000001302,  5.75537548503,      440.82528487760}, 
    {     0.00000001349,  2.49744006758,      984.60033162190}, 
    {     0.00000001355,  5.10790739045,      149.56319713460}, 
    {     0.00000001188,  2.24279457878,       31.49256938900}, 
    {     0.00000001231,  0.77900547379,      739.80866679490}, 
    {     0.00000001161,  3.10767970553,     2111.65031337760}, 
    {     0.00000001178,  4.30970344337,      561.93429400900}, 
    {     0.00000001233,  6.22576640438,     2214.74308759620}, 
    {     0.00000001095,  6.03022173687,     2737.32050569000}, 
    {     0.00000001324,  4.22919631556,     2538.24850425360}, 
    {     0.00000001346,  3.20576632074,      525.02509864860}, 
    {     0.00000001057,  5.76574985561,     2310.72231481400}, 
    {     0.00000001158,  0.46300827788,       67.66805156650}, 
    {     0.00000001027,  0.20709586018,        7.86430652620}, 
    {     0.00000001143,  5.56632279390,       46.47042291600}, 
    {     0.00000001012,  0.54307369204,      532.13864564940}, 
    {     0.00000000979,  5.14088953450,     2207.62954059540}, 
    {     0.00000000993,  2.03698162387,      319.57326339430}, 
    {     0.00000001035,  2.90325691870,      611.44309831080}, 
    {     0.00000001021,  4.75668560880,      527.24328453980}, 
    {     0.00000001310,  1.78907016216,      824.74219374880}, 
    {     0.00000000895,  2.54589419261,     2744.43405269080}, 
    {     0.00000000890,  5.41093971819,       28.45418800320}, 
    {     0.00000000985,  0.88687783832,     5760.49843189760}, 
    {     0.00000000983,  1.42102189882,     5746.27133789600}, 
    {     0.00000000893,  5.87175153771,      203.00415469950}, 
    {     0.00000000922,  4.17425091286,     2641.34127847220}, 
    {     0.00000000876,  0.75315488921,     1439.50969814920}, 
    {     0.00000000945,  2.31584676883,     9690.70812811720}, 
    {     0.00000000941,  2.84331047707,     9676.48103411560}, 
    {     0.00000000867,  0.81016495601,      524.27433912320}, 
    {     0.00000000828,  2.35268476661,      312.45971639350}, 
    {     0.00000000912,  2.80494184378,        6.21977512350}, 
    {     0.00000000808,  1.05165559697,      529.64278098480}, 
    {     0.00000000779,  4.79938843208,      945.24345570670}, 
    {     0.00000000878,  5.76532521399,        1.64453140270}, 
    {     0.00000000954,  4.30880174100,      209.36694217490}, 
    {     0.00000000772,  5.25564170894,     2950.61960112800}, 
    {     0.00000000745,  0.03807300102,      535.10759106600}, 
    {     0.00000000744,  0.58381523987,       25.27279426550}, 
    {     0.00000000735,  0.19889697619,     1049.08698945070}, 
    {     0.00000000747,  2.71776604422,       38.13303563780}, 
    {     0.00000000728,  5.97254317194,      945.99421523210}, 
    {     0.00000000769,  4.51524159414,      952.35700270750}, 
    {     0.00000000711,  0.38043574201,       69.15252427480}, 
    {     0.00000000761,  3.07043913906,       39.35687591520}, 
    {     0.00000000802,  1.14189803237,      532.61172640140}, 
    {     0.00000000704,  1.25543872788,      547.85021235930}, 
    {     0.00000000800,  3.20276130202,      604.47256366190}, 
    {     0.00000000821,  1.05238771575,      909.81873305460}, 
    {     0.00000000725,  5.68293554150,      953.10776223290}, 
    {     0.00000000682,  1.20168457647,      387.24131496080}, 
    {     0.00000000640,  3.91564016975,      528.72775724810}, 
    {     0.00000000663,  0.81538903178,     2228.97018159780}, 
    {     0.00000000808,  4.24946672460,      529.73914920440}, 
    {     0.00000000768,  0.58100515131,     2097.42321937600}, 
    {     0.00000000693,  2.51156186683,      916.93228005540}, 
    {     0.00000000784,  4.23618116997,      195.13984817330}, 
    {     0.00000000763,  1.12270397266,      732.69511979410}, 
    {     0.00000000617,  5.80980286923,      739.05790726950}, 
    {     0.00000000734,  4.24709115085,      760.25553592000}, 
    {     0.00000000592,  3.26062064584,      202.25339517410}, 
    {     0.00000000552,  5.83536244089,      526.77020378780}, 
    {     0.00000000714,  4.90042609368,     2751.54759969160}, 
    {     0.00000000640,  1.38548213559,      530.65417294110}, 
    {     0.00000000620,  3.01948741376,      902.70518605380}, 
    {     0.00000000722,  5.18172356552,        1.48447270830}, 
    {     0.00000000530,  5.96271879869,     2015.67108615980}, 
    {     0.00000000541,  3.78415919087,     2957.73314812880}, 
    {     0.00000000530,  6.10433734445,     2531.13495725280}, 
    {     0.00000000569,  4.12853081905,     2854.64037391020}, 
    {     0.00000000498,  4.62946077069,      934.94851496820}, 
    {     0.00000000523,  3.63882931609,      437.64389113990}, 
    {     0.00000000527,  5.80963579852,     3053.71237534660}, 
    {     0.00000000489,  5.93594675987,     3178.14579056760}, 
    {     0.00000000488,  4.99103190309,      483.22054217860}, 
    {     0.00000000487,  5.55239102762,     2627.11418447060}, 
    {     0.00000000478,  0.83306238983,     1603.29998928540}, 
    {     0.00000000487,  5.86510858429,      724.83081326790}, 
    {     0.00000000453,  0.61324874134,     1159.29331067010}, 
    {     0.00000000451,  2.28214016934,     3060.82592234740}, 
    {     0.00000000515,  4.78127185341,      447.79581952650}, 
    {     0.00000000537,  0.63663065397,     1354.43315884340}, 
    {     0.00000000461,  2.67886294351,     1021.24889455140}, 
    {     0.00000000450,  1.91049628603,      597.35901666110}, 
    {     0.00000000488,  5.56151436365,     2435.15573003500}, 
    {     0.00000000432,  3.64946046991,      313.21047591890}, 
    {     0.00000000435,  3.02448452708,      533.88375078860}, 
    {     0.00000000426,  5.07997231709,     2524.02141025200}, 
    {     0.00000000491,  3.59200148259,      230.56457082540}, 
    {     0.00000000503,  1.57595009240,      454.90936652730}, 
    {     0.00000000526,  2.02899667490,     1279.79457262800}, 
    {     0.00000000388,  5.58072092256,      731.94436026870}, 
    {     0.00000000449,  1.11025492739,       56.62235130260}, 
    {     0.00000000460,  4.42534443381,      462.02291352810}, 
    {     0.00000000495,  0.36191781331,     1251.34038462480}, 
    {     0.00000000398,  5.20119376110,     3267.01147078460}, 
    {     0.00000000416,  1.70821947228,      245.54242435240}, 
    {     0.00000000355,  1.65214516751,       78.71375183040}, 
    {     0.00000000366,  5.75203350764,     2847.52682690940}, 
    {     0.00000000403,  1.72240208145,     1141.13406340540}, 
    {     0.00000000334,  6.01033746350,      960.22130923370}, 
    {     0.00000000331,  1.74101810453,      490.33408917940}, 
    {     0.00000000314,  5.73955945935,     1158.54255114470}, 
    {     0.00000000389,  0.31258924956,     2413.81508903260}, 
    {     0.00000000328,  3.50753080884,     3274.12501778540}, 
    {     0.00000000349,  0.38232238589,     2332.06295581640}, 
    {     0.00000000300,  4.75999716377,      938.12990870590}, 
    {     0.00000000325,  0.54991590409,       43.28902917830}, 
    {     0.00000000288,  4.90497702380,     1357.61455258110}, 
    {     0.00000000304,  6.12658548685,     1262.38608488870}, 
    {     0.00000000285,  2.89817774175,      530.21222995640}, 
    {     0.00000000285,  4.56582790812,     1268.74887236410}, 
    {     0.00000000310,  4.69121773135,       76.26607127560}, 
    {     0.00000000278,  5.49867187248,      280.96714700450}, 
    {     0.00000000279,  4.66775152978,     1261.63532536330}, 
    {     0.00000000357,  5.45944338384,      113.38771495710}, 
    {     0.00000000300,  4.11291800981,     1048.33622992530}, 
    {     0.00000000283,  1.09440291187,     1512.80682400820}, 
    {     0.00000000326,  0.60265644873,      827.92358748650}, 
    {     0.00000000280,  2.64073976181,      373.01422095920}, 
    {     0.00000000267,  1.94524254858,     3377.21779200400}, 
    {     0.00000000283,  5.36501811239,     1165.65609814550}, 
    {     0.00000000281,  5.54752717581,     3370.10424500320}, 
    {     0.00000000269,  3.92616563946,       42.53826965290}, 
    {     0.00000000270,  4.93414229832,     1041.22268292450}, 
    {     0.00000000274,  1.86909714777,     2655.56837247380}, 
    {     0.00000000259,  2.56026215512,     9146.79006902100}, 
    {     0.00000000258,  5.96872448521,     1269.49963188950}, 
    {     0.00000000254,  1.35449984820,     1061.82961074400}, 
    {     0.00000000282,  3.01539201149,      320.32402291970}, 
    {     0.00000000272,  4.18505693688,     8624.21265092720}, 
    {     0.00000000245,  1.24462798353,      252.65597135320}, 
    {     0.00000000260,  4.32490177755,     4017.11507831800}, 
    {     0.00000000247,  3.83116540525,      327.43756992050}, 
    {     0.00000000264,  1.13298595860,     1969.20066324380}, 
    {     0.00000000291,  2.99706400538,     4694.00295470760}, 
    {     0.00000000223,  5.86659978015,     3914.02230409940}, 
    {     0.00000000241,  3.94118046972,     3171.03224356680}, 
    {     0.00000000228,  5.97829032334,      224.34479570190}, 
    {     0.00000000223,  6.19814052214,     3281.23856478620}, 
    {     0.00000000246,  2.91332083588,     1514.29129671650}, 
    {     0.00000000230,  2.20701513150,      850.01498801430}, 
    {     0.00000000270,  0.58233992630,     1592.25428902150}, 
    {     0.00000000236,  4.85450939183,     3583.40334044120}, 
    {     0.00000000237,  2.74342922621,     1912.57831194120}, 
    {     0.00000000276,  6.04560989855,     1069.67687092770}, 
    {     0.00000000254,  1.83831918853,     1593.00504854690}, 
    {     0.00000000214,  3.63754231115,     3803.81598288000}, 
    {     0.00000000210,  3.08485590783,     3590.51688744200}, 
    {     0.00000000260,  5.06089460492,     1059.43011429900}, 
    {     0.00000000227,  0.23394232373,     1670.82502850000}, 
    {     0.00000000246,  5.53873348349,     2840.41327990860}, 
    {     0.00000000206,  4.55330855600,      554.06998748280}, 
    {     0.00000000202,  1.32439444045,     4326.39340097380}, 
    {     0.00000000227,  0.78540105705,       59.80374504030}, 
    {     0.00000000258,  1.30854335630,     1493.09366806600}, 
    {     0.00000000199,  0.45118573624,      529.53090640020}, 
    {     0.00000000203,  4.16872110150,     4333.50694797460}, 
    {     0.00000000207,  0.07882551152,     5223.69391980220}, 
    {     0.00000000203,  2.87164861799,      505.31194270640}, 
    {     0.00000000197,  4.05755296915,     1064.04779663520}, 
    {     0.00000000196,  5.99844851675,     3597.63043444280}, 
    {     0.00000000199,  3.30501818656,     4120.20785253660}, 
    {     0.00000000194,  5.95526916809,       84.93352695390}, 
    {     0.00000000195,  4.77984803416,     1098.73880610440}, 
    {     0.00000000245,  0.01831767727,     1567.73225428140}, 
    {     0.00000000204,  3.81252652390,      530.44172462000}, 
    {     0.00000000210,  1.56035035567,      512.28247735530}, 
    {     0.00000000198,  3.54440293022,      529.85102378900}, 
    {     0.00000000266,  1.58071929624,      983.11585891360}, 
    {     0.00000000198,  0.30047978925,     1166.40685767090}, 
    {     0.00000000188,  0.90738705875,      135.33610313300}, 
    {     0.00000000256,  1.87162378257,     1289.94650101460}, 
    {     0.00000000190,  1.05137411074,     1884.12412393800}, 
    {     0.00000000178,  1.01108545550,    10206.17199921020}, 
    {     0.00000000189,  0.35186987278,     1372.59240610810}, 
    {     0.00000000218,  5.40858666125,      679.25416222920}, 
    {     0.00000000172,  4.35360474429,     1578.02719501990}, 
    {     0.00000000172,  0.28434115891,      494.26624244250}, 
    {     0.00000000206,  0.01485146863,     2730.20695868920}, 
    {     0.00000000176,  5.20619161648,     3686.49611465980}, 
    {     0.00000000173,  1.83493659695,      746.92221379570}, 
    {     0.00000000177,  0.49024580662,     1585.89150154610}, 
    {     0.00000000206,  5.22730929781,     3995.77443731560}, 
    {     0.00000000190,  4.99077882242,     3067.93946934820}, 
    {     0.00000000169,  2.57956666704,     9161.01716302260}, 
    {     0.00000000168,  6.15800395467,      970.51624997220}, 
    {     0.00000000165,  1.51795928301,     4010.00153131720}, 
    {     0.00000000189,  0.74735111652,     2545.36205125440}, 
    {     0.00000000173,  3.38232793511,      885.43971066640}, 
    {     0.00000000166,  1.54981367866,     1070.42763045310}, 
    {     0.00000000163,  2.27700702598,     1060.34513803570}, 
    {     0.00000000157,  1.23713010823,     5216.58037280140}, 
    {     0.00000000178,  5.39417024046,     3163.91869656600}, 
    {     0.00000000158,  3.90063523153,     3487.42411322340}, 
    {     0.00000000169,  5.91153502769,     1578.77795454530}, 
    {     0.00000000178,  5.51894552093,     2943.50605412720}, 
    {     0.00000000154,  4.52070366231,     1058.41872234270}, 
    {     0.00000000163,  0.80456433006,     1585.14074202070}, 
    {     0.00000000151,  4.87442909516,       81.89514556810}, 
    {     0.00000000180,  1.88055488803,      685.47393735270}, 
    {     0.00000000154,  3.65536637158,    77734.01845962799}, 
    {     0.00000000163,  5.06311074065,      498.67147645760}, 
    {     0.00000000162,  0.84216605238,     2200.51599359460}, 
    {     0.00000000189,  0.56636371283,      842.15068148810}, 
    {     0.00000000151,  4.66530832982,      977.48678462110}, 
    {     0.00000000187,  3.11784576157,      630.33605875840}, 
    {     0.00000000144,  0.70005415255,       92.79783348010}, 
    {     0.00000000138,  2.92367081829,      927.83496796740}, 
    {     0.00000000164,  3.73913227289,     1134.16352875650}, 
    {     0.00000000182,  5.86715864086,     5753.38488489680}, 
    {     0.00000000144,  4.89589455408,      991.71387862270}, 
    {     0.00000000137,  2.07768743239,      842.90144101350}, 
    {     0.00000000151,  2.10726170967,      860.30992875280}, 
    {     0.00000000140,  0.77231183403,     9683.59458111640}, 
    {     0.00000000131,  2.96777933087,      497.44763618020}, 
    {     0.00000000119,  1.26007410940,     2005.37614542130}, 
    {     0.00000000120,  6.13286906499,     1987.21689815660}, 
    {     0.00000000143,  2.40231943231,      529.16970023280}, 
    {     0.00000000113,  4.73094855840,     4863.19791306920}, 
    {     0.00000000122,  4.54364035076,     1371.84164658270}, 
    {     0.00000000135,  3.56089271537,     1054.71606374320}, 
    {     0.00000000115,  1.55810156690,     9153.90361602180}, 
    {     0.00000000150,  4.28443290371,      429.04587143080}, 
    {     0.00000000132,  5.07409771627,     1056.93424963440}, 
    {     0.00000000112,  4.59192248879,     3700.72320866140}, 
    {     0.00000000103,  2.60811213731,     1894.41906467650}, 
    {     0.00000000105,  5.94340093827,     1057.89745748090}, 
    {     0.00000000101,  1.58846813422,     3693.60966166060}, 
    {     0.00000000118,  4.88733637311,      600.54041039880}, 
    {     0.00000000098,  1.38793271630,     1059.33374607940}, 
    {     0.00000000100,  5.74975444020,      501.23677709140}, 
    {     0.00000000101,  0.02209271767,     2964.84669512960}, 
    {     0.00000000095,  0.49108484683,      560.71045373160}, 
    {     0.00000000094,  5.18380306247,     4546.80604341260}, 
    {     0.00000000104,  3.47229999154,     4223.30062675520}, 
    {     0.00000000099,  5.46359299375,     3156.80514956520}, 
    {     0.00000000099,  5.95584423449,      547.09945283390}, 
    {     0.00000000091,  1.87848199981,      528.94020556920}, 
    {     0.00000000108,  5.98018728055,     1364.72809958190}, 
    {     0.00000000116,  3.44357640421,     1432.39615114840}, 
    {     0.00000000088,  4.22154936325,     4649.89881763120}, 
    {     0.00000000109,  3.83768244476,      525.49817940060}, 
    {     0.00000000087,  0.58669584397,     1173.52040467170}, 
    {     0.00000000091,  5.33968822169,      216.48048917570}, 
    {     0.00000000102,  1.41480903153,     3075.05301634900}, 
    {     0.00000000102,  1.74475388738,     2758.66114669240}, 
    {     0.00000000089,  5.89316363283,      757.21715453420}, 
    {     0.00000000086,  6.04340651740,     6275.96230299060}, 
    {     0.00000000101,  4.70225529886,     3473.19701922180}, 
    {     0.00000000079,  5.72096488951,     5385.77533116300}, 
    {     0.00000000078,  1.11944499728,      429.77958461370}, 
    {     0.00000000078,  5.12580794008,     1475.68518032670}, 
    {     0.00000000078,  3.87444671518,     2321.76801507790}, 
    {     0.00000000086,  2.89392726975,    10213.28554621100}, 
    {     0.00000000077,  1.40171543677,     5179.58978272580}, 
    {     0.00000000076,  0.09895432561,     3707.83675566220}, 
    {     0.00000000073,  5.65154413109,     1151.42900414390}, 
    {     0.00000000084,  5.15227885953,     1091.62525910360}, 
    {     0.00000000079,  4.81154341200,     3384.33133900480}, 
    {     0.00000000080,  0.05190580386,     1080.72257119160}, 
    {     0.00000000080,  5.35119272632,        2.44768055480}, 
    {     0.00000000085,  5.88100684593,      234.63973644040}, 
};


static const struct ln_vsop jupiter_longitude_l2[LONG_L2] = {
    {     0.00047233601,  4.32148536482,        7.11354700080}, 
    {     0.00030649436,  2.92977788700,      529.69096509460}, 
    {     0.00014837605,  3.14159265359,        0.00000000000}, 
    {     0.00003189359,  1.05515491122,      522.57741809380}, 
    {     0.00002728901,  4.84555421873,      536.80451209540}, 
    {     0.00002547440,  3.42720888976,     1059.38193018920}, 
    {     0.00001721046,  4.18734600902,       14.22709400160}, 
    {     0.00000383277,  5.76794364868,      419.48464387520}, 
    {     0.00000367514,  6.05520169517,      103.09277421860}, 
    {     0.00000377503,  0.76050839060,      515.46387109300}, 
    {     0.00000337386,  3.78644856157,        3.18139373770}, 
    {     0.00000308194,  0.69368283790,      206.18554843720}, 
    {     0.00000214121,  3.82958181430,     1589.07289528380}, 
    {     0.00000203945,  5.34259263233,     1066.49547719000}, 
    {     0.00000197456,  2.48351071790,        3.93215326310}, 
    {     0.00000146156,  3.81335105293,      639.89728631400}, 
    {     0.00000156209,  1.36162315686,     1052.26838318840}, 
    {     0.00000129577,  5.83745710707,      412.37109687440}, 
    {     0.00000141825,  1.63491733107,      426.59819087600}, 
    {     0.00000117324,  1.41441723025,      625.67019231240}, 
    {     0.00000096673,  4.03472268105,      110.20632121940}, 
    {     0.00000090824,  1.10616181082,       95.97922721780}, 
    {     0.00000078757,  4.63773672633,      543.91805909620}, 
    {     0.00000072393,  2.21660922294,      735.87651353180}, 
    {     0.00000087320,  2.52152838765,      632.78373931320}, 
    {     0.00000056885,  3.12193937495,      213.29909543800}, 
    {     0.00000048615,  1.67250930065,      309.27832265580}, 
    {     0.00000058472,  0.83261136328,      199.07200143640}, 
    {     0.00000040161,  4.02477739294,       21.34064100240}, 
    {     0.00000039773,  0.62346681537,      323.50541665740}, 
    {     0.00000035738,  2.32587552001,      728.76296653100}, 
    {     0.00000025610,  2.52090555309,     1162.47470440780}, 
    {     0.00000029257,  3.60827234952,       10.29494073850}, 
    {     0.00000023621,  3.00418693282,      956.28915597060}, 
    {     0.00000027790,  3.24029772587,      838.96928775040}, 
    {     0.00000025988,  4.50541789846,      742.99006053260}, 
    {     0.00000025259,  1.21368179972,     1045.15483618760}, 
    {     0.00000019456,  4.29184444888,      532.87235883230}, 
    {     0.00000016160,  5.81618778562,     1596.18644228460}, 
    {     0.00000017655,  0.80915458780,      508.35032409220}, 
    {     0.00000017714,  4.21087482222,     2118.76386037840}, 
    {     0.00000016950,  1.83162996779,      526.50957135690}, 
    {     0.00000014656,  3.99869563261,      117.31986822020}, 
    {     0.00000013717,  1.80293013315,      302.16477565500}, 
    {     0.00000013232,  2.51839383442,       88.86568021700}, 
    {     0.00000012771,  4.36965277120,     1169.58825140860}, 
    {     0.00000015311,  0.68283508612,      942.06206196900}, 
    {     0.00000010924,  4.44465911708,      525.75881183150}, 
    {     0.00000013902,  5.95861098210,      316.39186965660}, 
    {     0.00000009462,  2.17903550202,     1155.36115740700}, 
    {     0.00000008792,  3.29010679292,      220.41264243880}, 
    {     0.00000007851,  5.76115179798,      846.08283475120}, 
    {     0.00000007640,  2.72045021550,      533.62311835770}, 
    {     0.00000009055,  1.63552089571,     1581.95934828300}, 
    {     0.00000008687,  3.31770180816,      831.85574074960}, 
    {     0.00000006355,  0.49733352086,      949.17560896980}, 
    {     0.00000006615,  2.18391508427,     1265.56747862640}, 
    {     0.00000005380,  6.00496610446,      405.25754987360}, 
    {     0.00000004562,  1.38462817429,     1258.45393162560}, 
    {     0.00000004367,  5.07489817646,     1073.60902419080}, 
    {     0.00000004280,  3.04118697325,     1692.16566950240}, 
    {     0.00000004371,  5.47491964600,      433.71173787680}, 
    {     0.00000004201,  5.28578420235,       18.15924726470}, 
    {     0.00000003950,  1.25151054185,      853.19638175200}, 
    {     0.00000005302,  3.65714557917,     1272.68102562720}, 
    {     0.00000004368,  2.27494144993,     1368.66025284500}, 
    {     0.00000003462,  1.50340907962,      519.39602435610}, 
    {     0.00000002757,  2.16577371531,     1478.86657406440}, 
    {     0.00000002704,  1.04777971186,     1574.84580128220}, 
    {     0.00000002891,  2.04866759038,     1361.54670584420}, 
    {     0.00000003075,  0.99105386830,      191.95845443560}, 
    {     0.00000002437,  2.36815291342,     1471.75302706360}, 
    {     0.00000002201,  2.47797001828,      721.64941953020}, 
    {     0.00000002093,  3.72335003599,     1485.98012106520}, 
    {     0.00000002273,  3.03212449012,     1148.24761040620}, 
    {     0.00000001947,  1.88764180020,     1685.05212250160}, 
    {     0.00000002057,  6.18001258073,      330.61896365820}, 
    {     0.00000001451,  4.72055072637,       32.24332891440}, 
    {     0.00000001449,  3.18799149050,      635.96513305090}, 
    {     0.00000001377,  5.12507193192,     1375.77379984580}, 
    {     0.00000001421,  1.99249188460,      629.60234557550}, 
    {     0.00000001401,  4.26834108454,      551.03160609700}, 
    {     0.00000001265,  0.00691519565,     2125.87740737920}, 
    {     0.00000001272,  2.25106018556,     1788.14489672020}, 
    {     0.00000001238,  1.75660677516,     1677.93857550080}, 
    {     0.00000001206,  2.18559244687,     1795.25844372100}, 
    {     0.00000001493,  4.02813570061,      539.98590583310}, 
    {     0.00000001314,  4.76481710487,     1062.56332392690}, 
    {     0.00000001110,  2.97713206981,       81.75213321620}, 
    {     0.00000001027,  1.99159218429,      295.05122865420}, 
    {     0.00000001368,  4.63088532557,     2648.45482547300}, 
    {     0.00000001025,  3.75336759986,       28.45418800320}, 
    {     0.00000000978,  3.01394148632,      124.43341522100}, 
    {     0.00000001227,  1.22879053363,     1038.04128918680}, 
    {     0.00000000965,  1.17674106025,       99.91138048090}, 
    {     0.00000001015,  1.85922216390,      750.10360753340}, 
    {     0.00000000924,  3.53294521831,      227.52618943960}, 
    {     0.00000000988,  5.05622576252,     1699.27921650320}, 
    {     0.00000001059,  0.13477400877,      416.30325013750}, 
    {     0.00000000819,  2.01948161630,     1056.20053645150}, 
    {     0.00000000888,  1.75920995401,     1898.35121793960}, 
    {     0.00000001013,  2.80784883642,     1464.63948006280}, 
    {     0.00000000791,  4.92419444433,     1055.44977692610}, 
    {     0.00000000774,  1.91132974373,     2111.65031337760}, 
    {     0.00000000729,  3.29016656970,      628.85158605010}, 
    {     0.00000000743,  2.65216075794,      106.27416795630}, 
    {     0.00000000719,  2.95858266157,     2008.55753915900}, 
    {     0.00000000693,  0.10835603179,      963.40270297140}, 
    {     0.00000000828,  2.72900314719,      618.55664531160}, 
    {     0.00000000777,  1.63387777696,     2001.44399215820}, 
    {     0.00000000651,  1.19267978130,      422.66603761290}, 
    {     0.00000000681,  5.47481858348,     5760.49843189760}, 
    {     0.00000000681,  3.11621018972,     5746.27133789600}, 
    {     0.00000000644,  4.68534695662,      611.44309831080}, 
    {     0.00000000665,  1.86713865983,     2104.53676637680}, 
    {     0.00000000629,  3.05748834184,      380.12776796000}, 
    {     0.00000000637,  1.85731506560,      636.71589257630}, 
    {     0.00000000715,  3.04974505007,     2221.85663459700}, 
    {     0.00000000635,  4.53916560604,     9676.48103411560}, 
    {     0.00000000635,  0.61458920732,     9690.70812811720}, 
    {     0.00000000821,  6.24663887828,      423.41679713830}, 
    {     0.00000000764,  4.32616763486,     1802.37199072180}, 
    {     0.00000000581,  0.83633087877,     1891.23767093880}, 
    {     0.00000000638,  2.83653046158,     1905.46476494040}, 
    {     0.00000000558,  3.96114629751,      440.82528487760}, 
    {     0.00000000623,  1.22711488010,     1382.88734684660}, 
    {     0.00000000711,  3.43507379865,      824.74219374880}, 
    {     0.00000000516,  1.10671630111,      107.02492748170}, 
    {     0.00000000535,  1.55914282530,     1994.33044515740}, 
    {     0.00000000548,  4.39997113815,      647.01083331480}, 
    {     0.00000000412,  1.25354625957,      203.00415469950}, 
    {     0.00000000414,  2.66777275564,     2324.94940881560}, 
    {     0.00000000533,  2.55533346856,     1781.03134971940}, 
    {     0.00000000393,  1.26401319046,      210.11770170030}, 
    {     0.00000000428,  1.47563898333,     2214.74308759620}, 
    {     0.00000000417,  2.88282194210,     1063.31408345230}, 
    {     0.00000000431,  5.00337132770,     3178.14579056760}, 
    {     0.00000000404,  3.51234818882,     2751.54759969160}, 
    {     0.00000000433,  4.29604508638,     5753.38488489680}, 
    {     0.00000000311,  0.32531359824,     2655.56837247380}, 
    {     0.00000000315,  0.16909542121,     1279.79457262800}, 
    {     0.00000000327,  3.36314839669,     1141.13406340540}, 
    {     0.00000000340,  1.47994765617,     2317.83586181480}, 
    {     0.00000000280,  5.45018668393,     2228.97018159780}, 
    {     0.00000000286,  1.69087245649,     2420.92863603340}, 
    {     0.00000000272,  0.27466300281,      319.57326339430}, 
    {     0.00000000285,  2.92648819935,     2957.73314812880}, 
    {     0.00000000242,  6.23321763999,      934.94851496820}, 
    {     0.00000000265,  0.35799742793,     2840.41327990860}, 
    {     0.00000000247,  2.41874119352,     1251.34038462480}, 
    {     0.00000000303,  2.43034117616,       70.84944530420}, 
    {     0.00000000251,  0.43544711316,     3259.89792378380}, 
    {     0.00000000226,  4.49396746521,     5223.69391980220}, 
    {     0.00000000233,  5.48382095726,     1603.29998928540}, 
    {     0.00000000272,  2.98590404673,     1457.52593306200}, 
    {     0.00000000285,  2.60754102796,     2538.24850425360}, 
    {     0.00000000207,  5.94297320087,     9153.90361602180}, 
    {     0.00000000283,  2.02857986620,     3171.03224356680}, 
    {     0.00000000291,  5.14022289511,     1592.25428902150}, 
    {     0.00000000233,  2.70967928648,     1354.43315884340}, 
    {     0.00000000268,  5.02822905034,     2015.67108615980}, 
    {     0.00000000239,  1.57690386034,     2744.43405269080}, 
    {     0.00000000284,  2.27103340038,     2854.64037391020}, 
    {     0.00000000254,  1.36546010277,     3370.10424500320}, 
    {     0.00000000221,  1.17223735868,     3053.71237534660}, 
    {     0.00000000224,  1.28623905132,     3060.82592234740}, 
    {     0.00000000205,  3.30510713580,     3384.33133900480}, 
    {     0.00000000222,  0.63302066932,     3163.91869656600}, 
    {     0.00000000188,  6.00513627145,       92.04707395470}, 
    {     0.00000000193,  1.57356589213,     2428.04218303420}, 
    {     0.00000000247,  2.25464204265,     2097.42321937600}, 
    {     0.00000000198,  2.56172919362,     2641.34127847220}, 
    {     0.00000000203,  3.40598495601,       99.16062095550}, 
    {     0.00000000179,  0.54218881357,     2207.62954059540}, 
    {     0.00000000178,  5.56443381281,     2332.06295581640}, 
    {     0.00000000176,  1.43070640110,      945.99421523210}, 
    {     0.00000000222,  3.66783138440,      113.38771495710}, 
    {     0.00000000178,  0.64947535071,     1176.70179840940}, 
    {     0.00000000199,  1.14834144531,     2531.13495725280}, 
    {     0.00000000166,  4.09266431951,     6283.07584999140}, 
    {     0.00000000183,  1.27422647789,     2310.72231481400}, 
    {     0.00000000227,  1.68715930646,     1567.73225428140}, 
    {     0.00000000188,  4.32227206118,     1069.67687092770}, 
    {     0.00000000225,  3.69300117786,     2435.15573003500}, 
    {     0.00000000162,  3.60183151152,     3067.93946934820}, 
    {     0.00000000203,  2.24205059922,       67.66805156650}, 
    {     0.00000000152,  5.48122906518,    10213.28554621100}, 
    {     0.00000000191,  2.68685722531,     1773.91780271860}, 
    {     0.00000000189,  2.95184731936,      732.69511979410}, 
    {     0.00000000178,  2.63197229299,     3274.12501778540}, 
    {     0.00000000168,  5.38131391591,     1585.14074202070}, 
    {     0.00000000152,  1.52826598178,     2950.61960112800}, 
    {     0.00000000172,  1.85377970325,     2413.81508903260}, 
    {     0.00000000165,  2.69610230323,      952.35700270750}, 
    {     0.00000000161,  4.77428302161,     1262.38608488870}, 
    {     0.00000000143,  6.22998196624,      860.30992875280}, 
    {     0.00000000187,  1.19805936589,     3362.99069800240}, 
    {     0.00000000134,  2.74105572000,     1670.82502850000}, 
    {     0.00000000122,  5.52449599842,      337.73251065900}, 
    {     0.00000000143,  1.20984019641,     2634.22773147140}, 
    {     0.00000000114,  2.52833228247,     1585.89150154610}, 
    {     0.00000000136,  2.69423835500,      739.80866679490}, 
    {     0.00000000112,  5.77394476974,      547.85021235930}, 
    {     0.00000000150,  4.91666030632,     3494.53766022420}, 
    {     0.00000000119,  5.50342415511,     4113.09430553580}, 
    {     0.00000000149,  0.81247034524,     3267.01147078460}, 
    {     0.00000000103,  0.80198707373,     2737.32050569000}, 
    {     0.00000000120,  2.81532905166,     3803.81598288000}, 
    {     0.00000000111,  2.44973721150,     3590.51688744200}, 
    {     0.00000000108,  1.33301085820,     1049.08698945070}, 
    {     0.00000000133,  0.33542188145,     3156.80514956520}, 
    {     0.00000000108,  2.55716124258,     4010.00153131720}, 
    {     0.00000000119,  1.02217622746,     2524.02141025200}, 
    {     0.00000000105,  5.89338290292,     3789.58888887840}, 
    {     0.00000000094,  0.88652607343,     3377.21779200400}, 
    {     0.00000000086,  1.26934319585,      511.53171782990}, 
    {     0.00000000082,  4.65514231193,     3281.23856478620}, 
    {     0.00000000081,  4.55655881694,     4319.27985397300}, 
    {     0.00000000084,  5.52322777064,     4120.20785253660}, 
    {     0.00000000075,  0.40562636382,     2627.11418447060}, 
    {     0.00000000099,  3.94867595848,     4017.11507831800}, 
    {     0.00000000080,  0.28157522970,     2847.52682690940}, 
    {     0.00000000073,  3.52191166845,     2964.84669512960}, 
    {     0.00000000092,  0.43014320279,     3914.02230409940}, 
    {     0.00000000083,  0.25202430423,     2644.52267220990}, 
};


static const struct ln_vsop jupiter_longitude_l3[LONG_L3] = {
    {     0.00006501673,  2.59862923650,        7.11354700080}, 
    {     0.00001355012,  1.34692775915,      529.69096509460}, 
    {     0.00000470691,  2.47502798748,       14.22709400160}, 
    {     0.00000416933,  3.24456258569,      536.80451209540}, 
    {     0.00000352870,  2.97380410245,      522.57741809380}, 
    {     0.00000165699,  2.09182221854,     1059.38193018920}, 
    {     0.00000086769,  2.51454300081,      515.46387109300}, 
    {     0.00000034458,  3.82181443085,     1066.49547719000}, 
    {     0.00000022671,  2.98178645046,      543.91805909620}, 
    {     0.00000023760,  1.27416115958,      412.37109687440}, 
    {     0.00000028501,  2.44538595164,      206.18554843720}, 
    {     0.00000019722,  2.10936654685,      639.89728631400}, 
    {     0.00000017778,  2.59019838502,     1589.07289528380}, 
    {     0.00000019709,  1.40149363982,      419.48464387520}, 
    {     0.00000018767,  1.58683219668,      103.09277421860}, 
    {     0.00000017015,  2.29975384867,       21.34064100240}, 
    {     0.00000016179,  3.15438287420,      625.67019231240}, 
    {     0.00000015902,  3.25713655347,     1052.26838318840}, 
    {     0.00000013421,  2.76078519881,       95.97922721780}, 
    {     0.00000013233,  2.53761666317,      199.07200143640}, 
    {     0.00000012676,  6.26512955217,      426.59819087600}, 
    {     0.00000008633,  2.26532712763,      110.20632121940}, 
    {     0.00000006718,  3.42006598208,      309.27832265580}, 
    {     0.00000008703,  1.76298942412,       10.29494073850}, 
    {     0.00000006529,  4.03744539112,      728.76296653100}, 
    {     0.00000005397,  5.26432570770,      323.50541665740}, 
    {     0.00000005685,  2.51772778746,      508.35032409220}, 
    {     0.00000007504,  0.00000000000,        0.00000000000}, 
    {     0.00000005431,  2.90223114269,     1045.15483618760}, 
    {     0.00000003997,  4.30231913648,       88.86568021700}, 
    {     0.00000003855,  3.52241347275,      302.16477565500}, 
    {     0.00000003811,  4.08897954122,      735.87651353180}, 
    {     0.00000003232,  1.47972151050,      956.28915597060}, 
    {     0.00000002931,  4.35694383564,     1596.18644228460}, 
    {     0.00000002657,  1.27257961451,      213.29909543800}, 
    {     0.00000002556,  2.23303484585,      117.31986822020}, 
    {     0.00000002414,  2.91828676420,      742.99006053260}, 
    {     0.00000002657,  5.01551013390,      838.96928775040}, 
    {     0.00000001935,  2.79590256973,     1169.58825140860}, 
    {     0.00000002222,  2.39310688825,      942.06206196900}, 
    {     0.00000001605,  3.09964511466,     2118.76386037840}, 
    {     0.00000001491,  1.55001725357,      220.41264243880}, 
    {     0.00000001934,  5.00823602310,      831.85574074960}, 
    {     0.00000001584,  1.40103448632,      405.25754987360}, 
    {     0.00000001286,  3.46966168288,     1073.60902419080}, 
    {     0.00000001210,  4.05719633951,     1155.36115740700}, 
    {     0.00000000995,  3.40755481322,      532.87235883230}, 
    {     0.00000000895,  1.64086921760,      632.78373931320}, 
    {     0.00000000942,  2.70150730852,      191.95845443560}, 
    {     0.00000000817,  3.29435640763,     1258.45393162560}, 
    {     0.00000000721,  1.62926029676,      949.17560896980}, 
    {     0.00000000745,  1.14787945018,     1162.47470440780}, 
    {     0.00000000719,  3.73992764870,      433.71173787680}, 
    {     0.00000000658,  2.90980216736,     1574.84580128220}, 
    {     0.00000000611,  5.95148659718,      853.19638175200}, 
    {     0.00000000665,  3.54820168197,      525.75881183150}, 
    {     0.00000000609,  4.14925115671,      721.64941953020}, 
    {     0.00000000598,  4.69470159905,       81.75213321620}, 
    {     0.00000000669,  1.94668551888,     1272.68102562720}, 
    {     0.00000000643,  2.02118053595,      526.50957135690}, 
    {     0.00000000508,  4.35239131420,     1368.66025284500}, 
    {     0.00000000509,  4.95261621008,     1148.24761040620}, 
    {     0.00000000564,  3.41879628800,     1581.95934828300}, 
    {     0.00000000512,  4.39016117028,      330.61896365820}, 
    {     0.00000000548,  2.25796919785,      551.03160609700}, 
    {     0.00000000478,  3.86015693760,     1361.54670584420}, 
    {     0.00000000383,  0.24286568335,      611.44309831080}, 
    {     0.00000000434,  2.94972316227,     1038.04128918680}, 
    {     0.00000000376,  1.42987791517,      124.43341522100}, 
    {     0.00000000390,  4.06059870551,     1471.75302706360}, 
    {     0.00000000385,  4.70313900114,      519.39602435610}, 
    {     0.00000000428,  2.22447290956,      539.98590583310}, 
    {     0.00000000394,  4.52891996323,     1464.63948006280}, 
    {     0.00000000306,  2.02015964470,     1485.98012106520}, 
    {     0.00000000283,  0.96808839854,     1905.46476494040}, 
    {     0.00000000278,  4.35223393872,      963.40270297140}, 
    {     0.00000000309,  3.65940227544,      846.08283475120}, 
    {     0.00000000342,  4.17369218547,     1788.14489672020}, 
    {     0.00000000259,  4.00812218110,     1265.56747862640}, 
    {     0.00000000293,  3.91258428829,     1685.05212250160}, 
    {     0.00000000259,  1.01628149559,     1478.86657406440}, 
    {     0.00000000253,  3.12703531515,     1994.33044515740}, 
    {     0.00000000238,  6.13097565419,     1382.88734684660}, 
    {     0.00000000220,  4.81059910221,     2125.87740737920}, 
    {     0.00000000225,  2.51478069462,     1891.23767093880}, 
    {     0.00000000278,  3.63969386282,     1677.93857550080}, 
    {     0.00000000242,  2.90163762388,     2310.72231481400}, 
    {     0.00000000242,  3.56541237319,     1699.27921650320}, 
    {     0.00000000248,  6.02173100984,      750.10360753340}, 
    {     0.00000000197,  5.17715231546,      618.55664531160}, 
    {     0.00000000256,  4.19052619061,     1781.03134971940}, 
    {     0.00000000196,  0.77278217513,     2221.85663459700}, 
    {     0.00000000185,  3.87563539893,      295.05122865420}, 
    {     0.00000000234,  2.54350140197,     1375.77379984580}, 
    {     0.00000000184,  3.72826587808,     2538.24850425360}, 
    {     0.00000000189,  5.74277274755,     2627.11418447060}, 
    {     0.00000000163,  1.29242716775,     1692.16566950240}, 
    {     0.00000000218,  3.86704847246,     2104.53676637680}, 
    {     0.00000000171,  5.25744961028,      824.74219374880}, 
    {     0.00000000171,  4.17086334577,     2097.42321937600}, 
    {     0.00000000149,  4.30563038349,     2001.44399215820}, 
    {     0.00000000148,  1.85615806078,     1056.20053645150}, 
    {     0.00000000155,  4.31124093129,     2317.83586181480}, 
    {     0.00000000152,  3.97372662088,     1055.44977692610}, 
    {     0.00000000147,  1.55828353595,      227.52618943960}, 
    {     0.00000000196,  2.21259819908,      934.94851496820}, 
    {     0.00000000160,  1.77096189842,     1141.13406340540}, 
    {     0.00000000132,  3.78618524413,     1062.56332392690}, 
    {     0.00000000179,  5.57450109164,     1354.43315884340}, 
    {     0.00000000121,  3.84004974551,     2634.22773147140}, 
    {     0.00000000118,  1.43347687364,     1279.79457262800}, 
    {     0.00000000124,  3.41965347556,     2648.45482547300}, 
    {     0.00000000162,  2.01594918927,      533.62311835770}, 
    {     0.00000000106,  3.26215180863,     2207.62954059540}, 
    {     0.00000000107,  0.88798638307,     1670.82502850000}, 
    {     0.00000000107,  0.60623932999,     2413.81508903260}, 
    {     0.00000000082,  0.40279200309,     2950.61960112800}, 
    {     0.00000000080,  2.06822079440,     3060.82592234740}, 
    {     0.00000000083,  2.43109843716,     2428.04218303420}, 
    {     0.00000000079,  3.80336766578,     1603.29998928540}, 
};


static const struct ln_vsop jupiter_longitude_l4[LONG_L4] = {
    {     0.00000669505,  0.85280378158,        7.11354700080}, 
    {     0.00000099965,  0.74243651986,       14.22709400160}, 
    {     0.00000050030,  1.65383477095,      536.80451209540}, 
    {     0.00000043690,  5.81923759985,      529.69096509460}, 
    {     0.00000031794,  4.85865051639,      522.57741809380}, 
    {     0.00000014735,  4.29065528652,      515.46387109300}, 
    {     0.00000008408,  0.68386181768,     1059.38193018920}, 
    {     0.00000004926,  1.29899425511,      543.91805909620}, 
    {     0.00000004563,  2.31453670801,     1066.49547719000}, 
    {     0.00000004254,  0.48193363691,       21.34064100240}, 
    {     0.00000003100,  3.00251285081,      412.37109687440}, 
    {     0.00000002053,  0.39854167561,      639.89728631400}, 
    {     0.00000001764,  4.90551864257,      625.67019231240}, 
    {     0.00000001901,  4.25660977930,      199.07200143640}, 
    {     0.00000001690,  4.25228443627,      206.18554843720}, 
    {     0.00000001345,  5.06309624095,     1052.26838318840}, 
    {     0.00000001211,  4.71432598740,       95.97922721780}, 
    {     0.00000001091,  1.32037613765,     1589.07289528380}, 
    {     0.00000000971,  5.67505418481,      728.76296653100}, 
    {     0.00000000935,  6.05626917469,       88.86568021700}, 
    {     0.00000000941,  4.66216576341,     1045.15483618760}, 
    {     0.00000000907,  4.56755235537,      426.59819087600}, 
    {     0.00000000783,  3.39826306476,      419.48464387520}, 
    {     0.00000000763,  3.50908239900,      103.09277421860}, 
    {     0.00000000737,  0.53486231851,      110.20632121940}, 
    {     0.00000000413,  5.21759457392,      302.16477565500}, 
    {     0.00000000397,  6.22333486636,      956.28915597060}, 
    {     0.00000000375,  5.22028842158,      309.27832265580}, 
    {     0.00000000357,  4.77132381360,      508.35032409220}, 
    {     0.00000000422,  0.58114211624,      117.31986822020}, 
    {     0.00000000318,  3.51963719294,      323.50541665740}, 
    {     0.00000000353,  4.07385033829,      942.06206196900}, 
    {     0.00000000318,  0.47985672138,      831.85574074960}, 
    {     0.00000000251,  1.79670889239,     1073.60902419080}, 
    {     0.00000000255,  2.93957928902,     1596.18644228460}, 
    {     0.00000000210,  0.42245785278,      220.41264243880}, 
    {     0.00000000188,  1.11282762167,     1169.58825140860}, 
    {     0.00000000187,  2.15988498485,     1361.54670584420}, 
    {     0.00000000180,  3.44457638757,     1148.24761040620}, 
    {     0.00000000157,  3.04524492827,     1272.68102562720}, 
    {     0.00000000173,  5.21493846901,     1581.95934828300}, 
    {     0.00000000160,  1.91340275752,     2118.76386037840}, 
    {     0.00000000194,  4.74134167991,     1155.36115740700}, 
    {     0.00000000119,  2.25819104081,      330.61896365820}, 
    {     0.00000000127,  1.67407621995,     1891.23767093880}, 
    {     0.00000000131,  0.52395207361,      551.03160609700}, 
    {     0.00000000099,  3.45749497992,      647.01083331480}, 
    {     0.00000000077,  3.29690316802,     1368.66025284500}, 
};


static const struct ln_vsop jupiter_longitude_l5[LONG_L5] = {
    {     0.00000049639,  5.25769924770,        7.11354700080}, 
    {     0.00000015775,  5.24859620238,       14.22709400160}, 
    {     0.00000004326,  0.02660738929,      536.80451209540}, 
    {     0.00000001573,  1.18411087933,      522.57741809380}, 
    {     0.00000000819,  5.86582284529,      543.91805909620}, 
    {     0.00000000724,  0.88277941285,      515.46387109300}, 
    {     0.00000000360,  0.78335749573,     1066.49547719000}, 
    {     0.00000000319,  5.73095137303,     1059.38193018920}, 
    {     0.00000000198,  0.04372566049,     1589.07289528380}, 
    {     0.00000000107,  0.09298499958,     1073.60902419080}, 
    {     0.00000000079,  6.16619004945,      529.69096509460}, 
};


static const struct ln_vsop jupiter_latitude_b0[LAT_B0] = {
    {     0.02268615702,  3.55852606721,      529.69096509460}, 
    {     0.00109971634,  3.90809347197,     1059.38193018920}, 
    {     0.00110090358,  0.00000000000,        0.00000000000}, 
    {     0.00008101428,  3.60509572885,      522.57741809380}, 
    {     0.00006043996,  4.25883108339,     1589.07289528380}, 
    {     0.00006437782,  0.30627119215,      536.80451209540}, 
    {     0.00001106880,  2.98534409520,     1162.47470440780}, 
    {     0.00000941651,  2.93619073963,     1052.26838318840}, 
    {     0.00000894088,  1.75447402715,        7.11354700080}, 
    {     0.00000767280,  2.15473604461,      632.78373931320}, 
    {     0.00000944328,  1.67522315024,      426.59819087600}, 
    {     0.00000684219,  3.67808774854,      213.29909543800}, 
    {     0.00000629223,  0.64343290020,     1066.49547719000}, 
    {     0.00000835861,  5.17881977810,      103.09277421860}, 
    {     0.00000531671,  2.70305944444,      110.20632121940}, 
    {     0.00000558524,  0.01354838161,      846.08283475120}, 
    {     0.00000464449,  1.17337267936,      949.17560896980}, 
    {     0.00000431072,  2.60825022780,      419.48464387520}, 
    {     0.00000351433,  4.61062966359,     2118.76386037840}, 
    {     0.00000123148,  3.34968047337,     1692.16566950240}, 
    {     0.00000115038,  5.04892367391,      316.39186965660}, 
    {     0.00000132159,  4.77816940380,      742.99006053260}, 
    {     0.00000103402,  2.31878940535,     1478.86657406440}, 
    {     0.00000116379,  1.38688268881,      323.50541665740}, 
    {     0.00000102420,  3.15294025567,     1581.95934828300}, 
    {     0.00000103762,  3.70104530617,      515.46387109300}, 
    {     0.00000078650,  3.98318863271,     1265.56747862640}, 
    {     0.00000069935,  2.56006243114,      956.28915597060}, 
    {     0.00000055597,  0.37501076637,     1375.77379984580}, 
    {     0.00000051986,  0.99006936413,     1596.18644228460}, 
    {     0.00000055194,  0.40176641060,      525.75881183150}, 
    {     0.00000063456,  4.50073545366,      735.87651353180}, 
    {     0.00000049691,  0.18650769854,      543.91805909620}, 
    {     0.00000048831,  3.57260516733,      533.62311835770}, 
    {     0.00000028353,  1.53532751494,      625.67019231240}, 
    {     0.00000029209,  5.43144706118,      206.18554843720}, 
    {     0.00000023255,  5.95197656622,      838.96928775040}, 
    {     0.00000022841,  6.19262795963,      532.87235883230}, 
    {     0.00000023202,  4.06473393382,      526.50957135690}, 
    {     0.00000024435,  6.10948089320,     1169.58825140860}, 
    {     0.00000021116,  4.96322450112,     2648.45482547300}, 
    {     0.00000017878,  3.08705078418,     1795.25844372100}, 
    {     0.00000016234,  4.83514182468,     1368.66025284500}, 
    {     0.00000021314,  2.69476772406,     1045.15483618760}, 
    {     0.00000015740,  1.15129718235,      942.06206196900}, 
    {     0.00000017325,  1.61549112201,       14.22709400160}, 
    {     0.00000013396,  2.30541502374,      853.19638175200}, 
    {     0.00000011904,  3.09812644271,     2111.65031337760}, 
    {     0.00000011734,  2.83005459062,     2008.55753915900}, 
    {     0.00000011291,  0.98958488237,      433.71173787680}, 
    {     0.00000011830,  4.76527289406,      309.27832265580}, 
    {     0.00000010702,  3.70182977140,     2221.85663459700}, 
    {     0.00000010815,  5.81960671820,     1272.68102562720}, 
    {     0.00000013505,  3.28127499147,     1155.36115740700}, 
    {     0.00000010179,  2.58690544075,      117.31986822020}, 
    {     0.00000010632,  5.23488821353,       95.97922721780}, 
    {     0.00000008770,  0.40456977116,      220.41264243880}, 
    {     0.00000007439,  2.94640424217,      412.37109687440}, 
    {     0.00000006151,  2.69098997815,      380.12776796000}, 
    {     0.00000005028,  0.72749683440,     1055.44977692610}, 
    {     0.00000004939,  0.73757027802,     1905.46476494040}, 
    {     0.00000005421,  4.08611312731,     1685.05212250160}, 
    {     0.00000005936,  4.32059794159,     1063.31408345230}, 
    {     0.00000004737,  4.09302873263,      527.24328453980}, 
    {     0.00000004010,  0.51536205068,     1073.60902419080}, 
    {     0.00000004709,  1.84069593466,      984.60033162190}, 
    {     0.00000003974,  1.33608144666,     2125.87740737920}, 
    {     0.00000003762,  3.58647029066,      529.73914920440}, 
    {     0.00000004731,  6.16377395837,      532.13864564940}, 
    {     0.00000004666,  5.88761580267,      639.89728631400}, 
    {     0.00000003763,  0.38865915086,      529.64278098480}, 
    {     0.00000003409,  4.05403520743,     1898.35121793960}, 
    {     0.00000003458,  3.43863446426,     1485.98012106520}, 
    {     0.00000004230,  2.23769605857,       74.78159856730}, 
    {     0.00000003091,  0.16468497073,     1699.27921650320}, 
    {     0.00000002976,  0.72268932553,      530.65417294110}, 
    {     0.00000003162,  1.25051775753,      330.61896365820}, 
    {     0.00000002727,  4.37684648696,      149.56319713460}, 
    {     0.00000002837,  0.05988888469,     1439.50969814920}, 
    {     0.00000002983,  3.25251234697,      528.72775724810}, 
    {     0.00000002232,  0.26152702827,     1062.56332392690}, 
    {     0.00000002464,  1.16914990320,      453.42489381900}, 
    {     0.00000002596,  3.30503237792,     2324.94940881560}, 
    {     0.00000001988,  2.85269753342,     1574.84580128220}, 
    {     0.00000002527,  5.94464299442,      909.81873305460}, 
    {     0.00000002269,  1.30385144361,        3.93215326310}, 
    {     0.00000001742,  4.49934387430,     1258.45393162560}, 
    {     0.00000001714,  4.12970162252,     2001.44399215820}, 
    {     0.00000002028,  3.97933364572,     1056.20053645150}, 
    {     0.00000001667,  0.36035632569,    10213.28554621100}, 
    {     0.00000001579,  6.11636481584,     1802.37199072180}, 
    {     0.00000001393,  3.69324297104,     2214.74308759620}, 
    {     0.00000001604,  1.98841976369,       38.13303563780}, 
    {     0.00000001325,  1.74025919863,      529.16970023280}, 
    {     0.00000001451,  2.39820472604,     2428.04218303420}, 
    {     0.00000001594,  2.07557781162,     1021.24889455140}, 
    {     0.00000001319,  1.33764254668,      618.55664531160}, 
    {     0.00000001346,  3.27611250994,     2641.34127847220}, 
    {     0.00000001230,  0.19547016795,      305.34616939270}, 
    {     0.00000001223,  2.86673324041,     1382.88734684660}, 
    {     0.00000001324,  2.23549334986,      530.21222995640}, 
    {     0.00000001056,  3.80584206280,       76.26607127560}, 
    {     0.00000001050,  4.68049393704,     1788.14489672020}, 
    {     0.00000001226,  5.34004079561,     3178.14579056760}, 
    {     0.00000001009,  3.19598679941,     2538.24850425360}, 
    {     0.00000001266,  3.04716587183,      604.47256366190}, 
    {     0.00000000954,  3.86982853835,      728.76296653100}, 
    {     0.00000001124,  1.59536330231,        3.18139373770}, 
    {     0.00000000978,  0.25225276132,      983.11585891360}, 
    {     0.00000000948,  0.21562638606,      750.10360753340}, 
    {     0.00000000946,  3.93927018641,      508.35032409220}, 
    {     0.00000000920,  1.14676177277,      963.40270297140}, 
    {     0.00000000817,  5.93843083013,      831.85574074960}, 
    {     0.00000000770,  2.96062737592,      526.77020378780}, 
    {     0.00000001018,  5.55723104876,      199.07200143640}, 
    {     0.00000000761,  1.38163787157,      532.61172640140}, 
    {     0.00000000726,  3.98350624153,     2317.83586181480}, 
    {     0.00000000863,  0.87983185587,      490.33408917940}, 
    {     0.00000000868,  3.44355447829,      569.04784100980}, 
    {     0.00000000711,  4.11083927584,     2751.54759969160}, 
    {     0.00000000708,  0.33555577415,      528.94020556920}, 
    {     0.00000000708,  4.00539820601,      530.44172462000}, 
    {     0.00000000656,  4.39587636715,      519.39602435610}, 
    {     0.00000000801,  4.03968735657,     1364.72809958190}, 
    {     0.00000000679,  1.18645749024,      525.49817940060}, 
    {     0.00000000645,  5.10528821006,     1361.54670584420}, 
    {     0.00000000668,  3.15607509055,      533.88375078860}, 
    {     0.00000000663,  0.73722024842,     5223.69391980220}, 
    {     0.00000000663,  1.57092786810,     6283.07584999140}, 
    {     0.00000000543,  0.26361339096,      227.52618943960}, 
    {     0.00000000525,  6.22337510612,      539.98590583310}, 
    {     0.00000000513,  4.98311290285,      302.16477565500}, 
    {     0.00000000544,  2.22253022770,     2744.43405269080}, 
    {     0.00000000531,  2.62394469648,       99.16062095550}, 
    {     0.00000000602,  1.56087341101,      454.90936652730}, 
    {     0.00000000518,  0.26343809435,      551.03160609700}, 
    {     0.00000000516,  1.09334875112,      934.94851496820}, 
    {     0.00000000659,  0.62609803674,     1512.80682400820}, 
    {     0.00000000524,  0.64710955846,      524.06189080210}, 
    {     0.00000000516,  3.69478866795,      535.32003938710}, 
    {     0.00000000491,  3.63015352701,     2531.13495725280}, 
    {     0.00000000570,  0.61976758778,      540.73666535850}, 
    {     0.00000000496,  2.19397054688,     1514.29129671650}, 
    {     0.00000000532,  0.20040217534,      525.02509864860}, 
    {     0.00000000449,  0.62392433691,      529.53090640020}, 
    {     0.00000000449,  3.71676131146,      529.85102378900}, 
    {     0.00000000493,  0.39157407639,      224.34479570190}, 
    {     0.00000000450,  5.02496027796,     1048.33622992530}, 
    {     0.00000000428,  5.44829085911,       11.04570026390}, 
    {     0.00000000499,  4.13924061941,      534.35683154060}, 
    {     0.00000000528,  1.76471074936,      524.27433912320}, 
    {     0.00000000454,  4.53329910309,     1056.93424963440}, 
    {     0.00000000520,  2.57406093768,      535.10759106600}, 
    {     0.00000000398,  1.40335768867,      960.22130923370}, 
    {     0.00000000457,  4.17698500570,     2104.53676637680}, 
    {     0.00000000505,  5.36536006721,     1057.89745748090}, 
    {     0.00000000536,  4.80412344518,     1593.00504854690}, 
    {     0.00000000415,  0.96574631343,     2435.15573003500}, 
    {     0.00000000518,  0.54534019245,     1061.82961074400}, 
    {     0.00000000359,  4.02703442030,     1059.43011429900}, 
    {     0.00000000357,  2.66856274985,      835.03713448730}, 
    {     0.00000000443,  5.27506751917,        1.48447270830}, 
    {     0.00000000358,  5.94447745169,      440.82528487760}, 
    {     0.00000000471,  6.05795526096,     1471.75302706360}, 
    {     0.00000000386,  2.15957649340,     9153.90361602180}, 
    {     0.00000000424,  2.70933415956,     1038.04128918680}, 
    {     0.00000000359,  0.82921825054,     1059.33374607940}, 
    {     0.00000000310,  0.88102053266,      529.90341341570}, 
    {     0.00000000310,  3.45966511571,      529.47851677350}, 
    {     0.00000000300,  3.70314980875,     2634.22773147140}, 
    {     0.00000000292,  2.63690294080,      415.55249061210}, 
    {     0.00000000279,  1.60721363324,      643.82943957710}, 
    {     0.00000000291,  5.83172186169,     1148.24761040620}, 
    {     0.00000000370,  5.71572992264,      531.17543780290}, 
    {     0.00000000267,  5.39229778002,     1891.23767093880}, 
    {     0.00000000275,  3.34111459961,      518.64526483070}, 
    {     0.00000000269,  1.06062338999,     1585.14074202070}, 
    {     0.00000000305,  2.50290530704,      511.53171782990}, 
    {     0.00000000295,  1.84394223501,      547.85021235930}, 
    {     0.00000000254,  2.98339664362,     1134.16352875650}, 
    {     0.00000000289,  1.86077249808,       21.34064100240}, 
    {     0.00000000265,  4.93074056536,      679.25416222920}, 
    {     0.00000000250,  0.42864032040,     1969.20066324380}, 
    {     0.00000000308,  2.67241191564,     2957.73314812880}, 
    {     0.00000000222,  4.78828764413,      514.71311156760}, 
    {     0.00000000313,  4.88100504465,      528.20649238630}, 
    {     0.00000000221,  4.32945667530,     1677.93857550080}, 
    {     0.00000000217,  3.46325099644,     2950.61960112800}, 
    {     0.00000000216,  0.52215246917,     2228.97018159780}, 
    {     0.00000000214,  5.83569926578,      544.66881862160}, 
    {     0.00000000283,  2.88733008413,       35.42472265210}, 
    {     0.00000000272,  1.65636249662,     3060.82592234740}, 
    {     0.00000000234,  1.68821601235,     2655.56837247380}, 
    {     0.00000000205,  3.36180409781,     2847.52682690940}, 
    {     0.00000000264,  3.62728688214,     2420.92863603340}, 
    {     0.00000000191,  4.26801797983,      430.53034413910}, 
    {     0.00000000179,  3.91470663032,     3340.61242669980}, 
    {     0.00000000180,  0.04748930181,      387.24131496080}, 
    {     0.00000000241,  4.03850570457,      494.26624244250}, 
    {     0.00000000177,  4.26408822698,      672.14061522840}, 
    {     0.00000000187,  2.72585227782,      299.12639426920}, 
    {     0.00000000234,  1.34461198439,      173.94221952280}, 
    {     0.00000000171,  0.85583570724,     1603.29998928540}, 
    {     0.00000000224,  0.33038256827,      565.11568774670}, 
    {     0.00000000200,  1.27568775106,       39.35687591520}, 
    {     0.00000000170,  4.96553772568,     1464.63948006280}, 
    {     0.00000000211,  1.00937080256,      523.54062594030}, 
    {     0.00000000210,  3.75802767164,     2854.64037391020}, 
    {     0.00000000162,  5.87799218214,     3480.31056622260}, 
    {     0.00000000163,  4.62924224205,     2015.67108615980}, 
    {     0.00000000191,  3.33159283750,      535.84130424890}, 
    {     0.00000000151,  1.17104489977,     1060.34513803570}, 
    {     0.00000000160,  1.81868596669,      312.45971639350}, 
    {     0.00000000158,  2.59595816107,      529.43033266370}, 
    {     0.00000000158,  1.74472748730,      529.95159752550}, 
    {     0.00000000173,  3.62448533343,      230.56457082540}, 
    {     0.00000000142,  0.70435921398,      522.52923398400}, 
    {     0.00000000144,  5.35713735269,      107.02492748170}, 
    {     0.00000000144,  6.14090754307,     1158.54255114470}, 
    {     0.00000000178,  0.27468100074,     3906.90875709860}, 
    {     0.00000000126,  5.15022690251,     2207.62954059540}, 
    {     0.00000000126,  3.42007113405,        2.44768055480}, 
    {     0.00000000127,  0.39943436855,       70.84944530420}, 
    {     0.00000000123,  4.77863018783,     2524.02141025200}, 
    {     0.00000000123,  0.46252835423,      647.01083331480}, 
    {     0.00000000144,  3.60266428249,     1058.41872234270}, 
    {     0.00000000158,  3.76145245959,       92.04707395470}, 
    {     0.00000000119,  4.08254103435,     1585.89150154610}, 
    {     0.00000000125,  2.35595591495,     3163.91869656600}, 
    {     0.00000000122,  3.21032018083,     3377.21779200400}, 
    {     0.00000000121,  3.39767154960,       18.15924726470}, 
    {     0.00000000131,  1.67909216935,     1289.94650101460}, 
    {     0.00000000115,  2.35736056408,     1550.93985964600}, 
    {     0.00000000126,  2.40837527327,      106.27416795630}, 
    {     0.00000000131,  1.37643228010,     1023.95720753710}, 
    {     0.00000000121,  1.60251352962,       10.29494073850}, 
    {     0.00000000121,  0.61425825680,     1592.25428902150}, 
    {     0.00000000135,  3.60014547346,      124.43341522100}, 
    {     0.00000000137,  2.41776488975,     3274.12501778540}, 
    {     0.00000000129,  0.09688303813,     2332.06295581640}, 
    {     0.00000000092,  4.89058170259,     1098.73880610440}, 
    {     0.00000000106,  5.18592950792,     2281.23049651060}, 
    {     0.00000000114,  2.96580552116,     1166.40685767090}, 
    {     0.00000000092,  1.65027422750,      860.30992875280}, 
    {     0.00000000102,  3.64265158080,     3171.03224356680}, 
    {     0.00000000103,  1.63123525514,     1894.41906467650}, 
    {     0.00000000080,  0.38766601962,     4694.00295470760}, 
    {     0.00000000074,  3.86945907800,     3067.93946934820}, 
    {     0.00000000095,  1.66457947000,     1151.42900414390}, 
};


static const struct ln_vsop jupiter_latitude_b1[LAT_B1] = {
    {     0.00078203446,  1.52377859742,      529.69096509460}, 
    {     0.00007789905,  2.59734071843,     1059.38193018920}, 
    {     0.00002788602,  4.85622679819,      536.80451209540}, 
    {     0.00002429728,  5.45947255041,      522.57741809380}, 
    {     0.00001985777,  0.00000000000,        0.00000000000}, 
    {     0.00000711633,  3.13688338277,     1589.07289528380}, 
    {     0.00000292916,  5.27960297214,     1066.49547719000}, 
    {     0.00000257804,  4.76667796123,     1052.26838318840}, 
    {     0.00000271233,  0.10154920958,        7.11354700080}, 
    {     0.00000086261,  1.08347893125,      103.09277421860}, 
    {     0.00000079683,  1.04738628033,      110.20632121940}, 
    {     0.00000081369,  0.63901209639,      419.48464387520}, 
    {     0.00000081666,  0.49217368092,      426.59819087600}, 
    {     0.00000070613,  2.82219329635,      632.78373931320}, 
    {     0.00000066992,  5.48215719084,      515.46387109300}, 
    {     0.00000058497,  3.56648086507,     2118.76386037840}, 
    {     0.00000051976,  2.85910965609,      949.17560896980}, 
    {     0.00000041188,  4.75217333048,      543.91805909620}, 
    {     0.00000039924,  3.92433787110,      735.87651353180}, 
    {     0.00000040237,  1.13564290140,     1162.47470440780}, 
    {     0.00000026065,  5.69856804584,     1596.18644228460}, 
    {     0.00000031305,  6.03167547323,      323.50541665740}, 
    {     0.00000030485,  5.98342688371,      316.39186965660}, 
    {     0.00000021243,  4.88358142951,      213.29909543800}, 
    {     0.00000017336,  1.63355193402,      956.28915597060}, 
    {     0.00000016318,  1.68217979523,      206.18554843720}, 
    {     0.00000021612,  4.90561988011,     1581.95934828300}, 
    {     0.00000015050,  4.62184858700,      525.75881183150}, 
    {     0.00000015354,  4.38535188227,      532.87235883230}, 
    {     0.00000014194,  5.89751177643,      526.50957135690}, 
    {     0.00000012259,  5.76584367807,      533.62311835770}, 
    {     0.00000013752,  4.43118193299,     1045.15483618760}, 
    {     0.00000010998,  3.66464772481,      742.99006053260}, 
    {     0.00000010324,  4.35223675725,     1169.58825140860}, 
    {     0.00000012020,  6.22841485051,       14.22709400160}, 
    {     0.00000008201,  5.61044388483,     1265.56747862640}, 
    {     0.00000009125,  2.07963809004,     1692.16566950240}, 
    {     0.00000006995,  3.68757029433,      625.67019231240}, 
    {     0.00000006623,  2.95794554141,      942.06206196900}, 
    {     0.00000006854,  4.86899700840,     1155.36115740700}, 
    {     0.00000005392,  0.92120894811,      117.31986822020}, 
    {     0.00000004948,  5.58428784853,      433.71173787680}, 
    {     0.00000005907,  4.00891325053,      639.89728631400}, 
    {     0.00000004904,  0.79623393478,       95.97922721780}, 
    {     0.00000004849,  0.77150458453,      853.19638175200}, 
    {     0.00000004554,  3.96028178465,     2648.45482547300}, 
    {     0.00000003572,  5.03591772370,      220.41264243880}, 
    {     0.00000003471,  5.13166913050,     1073.60902419080}, 
    {     0.00000003611,  1.57140411443,     1478.86657406440}, 
    {     0.00000002856,  4.67088931160,     1272.68102562720}, 
    {     0.00000003393,  5.57286071973,     1375.77379984580}, 
    {     0.00000002753,  0.68101124197,      846.08283475120}, 
    {     0.00000002097,  6.16024347671,     2125.87740737920}, 
    {     0.00000002114,  5.87434713206,      330.61896365820}, 
    {     0.00000001945,  0.99530094399,      309.27832265580}, 
    {     0.00000001637,  0.11662674189,     1795.25844372100}, 
    {     0.00000001899,  5.04072957525,      412.37109687440}, 
    {     0.00000001791,  2.71494717262,     1485.98012106520}, 
    {     0.00000001543,  4.89349278048,     1062.56332392690}, 
    {     0.00000001379,  4.78442752303,     1699.27921650320}, 
    {     0.00000001614,  5.31695012950,     2111.65031337760}, 
    {     0.00000001356,  5.09369131122,     1055.44977692610}, 
    {     0.00000001472,  4.55646132730,     1574.84580128220}, 
    {     0.00000001216,  5.83778167217,     1258.45393162560}, 
    {     0.00000001061,  0.21929903524,     1063.31408345230}, 
    {     0.00000001281,  2.63291136301,     2221.85663459700}, 
    {     0.00000001282,  4.40670408797,      728.76296653100}, 
    {     0.00000001081,  5.65958153020,      508.35032409220}, 
    {     0.00000001236,  5.79698189268,     1056.20053645150}, 
    {     0.00000000834,  5.66034576977,      838.96928775040}, 
    {     0.00000000843,  1.39726903288,      199.07200143640}, 
    {     0.00000001114,  0.93457172591,     1368.66025284500}, 
    {     0.00000001004,  1.88230290234,     2008.55753915900}, 
    {     0.00000000784,  3.98772675676,     1471.75302706360}, 
    {     0.00000000682,  6.16172441549,      519.39602435610}, 
    {     0.00000000649,  3.11256832821,      618.55664531160}, 
    {     0.00000000597,  4.81489778721,      551.03160609700}, 
    {     0.00000000546,  4.76855837933,     1685.05212250160}, 
    {     0.00000000546,  4.45547174659,      539.98590583310}, 
    {     0.00000000628,  0.06358024238,        3.18139373770}, 
    {     0.00000000514,  1.39819252269,     1382.88734684660}, 
    {     0.00000000546,  5.95490984957,     1905.46476494040}, 
    {     0.00000000432,  4.90782507942,      227.52618943960}, 
    {     0.00000000375,  6.13692411934,     2428.04218303420}, 
    {     0.00000000441,  4.43503611535,     1038.04128918680}, 
    {     0.00000000336,  4.15259691191,      440.82528487760}, 
    {     0.00000000392,  4.41318281175,     1802.37199072180}, 
    {     0.00000000336,  1.95113506965,      525.02509864860}, 
    {     0.00000000322,  2.38708525663,      534.35683154060}, 
    {     0.00000000411,  4.66598314047,      750.10360753340}, 
    {     0.00000000270,  4.34851907328,     3178.14579056760}, 
    {     0.00000000344,  2.88739614093,        3.93215326310}, 
    {     0.00000000306,  0.14928179595,       21.34064100240}, 
    {     0.00000000229,  4.71494574126,     1788.14489672020}, 
    {     0.00000000253,  5.97477420709,     1898.35121793960}, 
    {     0.00000000220,  1.65244409667,      302.16477565500}, 
    {     0.00000000200,  5.63991949724,      524.27433912320}, 
    {     0.00000000197,  4.98395147244,      535.10759106600}, 
    {     0.00000000189,  1.27085486089,      831.85574074960}, 
    {     0.00000000217,  5.72813758318,      963.40270297140}, 
    {     0.00000000163,  4.41162044978,      511.53171782990}, 
    {     0.00000000157,  6.22659623699,      547.85021235930}, 
    {     0.00000000156,  4.47889955750,     2104.53676637680}, 
    {     0.00000000158,  4.68155089578,      526.77020378780}, 
    {     0.00000000157,  5.94254789616,      532.61172640140}, 
    {     0.00000000177,  1.54590155579,     2324.94940881560}, 
    {     0.00000000159,  0.57726792367,     1361.54670584420}, 
    {     0.00000000143,  5.47600559579,     1603.29998928540}, 
    {     0.00000000144,  1.09752516756,       74.78159856730}, 
    {     0.00000000125,  4.04792462029,     2001.44399215820}, 
    {     0.00000000116,  0.20661426580,     2655.56837247380}, 
    {     0.00000000100,  5.29546864010,     1891.23767093880}, 
    {     0.00000000104,  6.06015582682,       10.29494073850}, 
    {     0.00000000122,  3.06889841223,     2317.83586181480}, 
    {     0.00000000106,  3.07515212924,     2751.54759969160}, 
    {     0.00000000123,  3.57772593687,     2015.67108615980}, 
    {     0.00000000080,  5.22386963290,     2228.97018159780}, 
    {     0.00000000103,  2.60543230206,     2538.24850425360}, 
    {     0.00000000076,  6.05570454898,      984.60033162190}, 
    {     0.00000000087,  4.53831014475,     1148.24761040620}, 
};


static const struct ln_vsop jupiter_latitude_b2[LAT_B2] = {
    {     0.00005498320,  3.01596270062,      529.69096509460}, 
    {     0.00000602076,  3.13358939436,      536.80451209540}, 
    {     0.00000502174,  2.05202111599,     1059.38193018920}, 
    {     0.00000453862,  0.95912416388,      522.57741809380}, 
    {     0.00000115043,  0.00000000000,        0.00000000000}, 
    {     0.00000068911,  3.65515676096,     1066.49547719000}, 
    {     0.00000067052,  2.23363751256,     1589.07289528380}, 
    {     0.00000042555,  0.52143365809,     1052.26838318840}, 
    {     0.00000039396,  4.65314230657,        7.11354700080}, 
    {     0.00000023438,  0.96725852073,      515.46387109300}, 
    {     0.00000017383,  3.03116251890,      543.91805909620}, 
    {     0.00000006651,  4.14899100562,     1596.18644228460}, 
    {     0.00000007013,  2.58268666095,     2118.76386037840}, 
    {     0.00000005389,  5.43989474079,      110.20632121940}, 
    {     0.00000004578,  6.21390672967,     1045.15483618760}, 
    {     0.00000004226,  2.60174767485,      532.87235883230}, 
    {     0.00000003653,  5.49147329377,      426.59819087600}, 
    {     0.00000004208,  4.53565061928,       14.22709400160}, 
    {     0.00000003620,  2.16725398015,     1162.47470440780}, 
    {     0.00000004347,  4.34610976020,      323.50541665740}, 
    {     0.00000003449,  1.44287034922,      526.50957135690}, 
    {     0.00000003250,  4.99793920041,      632.78373931320}, 
    {     0.00000003549,  5.47945408971,      103.09277421860}, 
    {     0.00000003031,  0.65632340107,     1581.95934828300}, 
    {     0.00000003252,  5.38360789595,      949.17560896980}, 
    {     0.00000002464,  0.29383438152,      956.28915597060}, 
    {     0.00000002590,  2.61624183669,      525.75881183150}, 
    {     0.00000002414,  6.08828067002,      419.48464387520}, 
    {     0.00000002206,  2.62381175358,     1169.58825140860}, 
    {     0.00000001991,  1.56606451610,      533.62311835770}, 
    {     0.00000001868,  2.03564229490,      316.39186965660}, 
    {     0.00000002225,  6.11348450922,      735.87651353180}, 
    {     0.00000001512,  4.74989508185,      942.06206196900}, 
    {     0.00000001458,  3.53705002363,     1073.60902419080}, 
    {     0.00000001473,  3.61629070367,      206.18554843720}, 
    {     0.00000001467,  5.52885404945,      117.31986822020}, 
    {     0.00000001373,  0.36875884830,     1155.36115740700}, 
    {     0.00000001237,  2.65571662403,       95.97922721780}, 
    {     0.00000001124,  3.90568585311,      433.71173787680}, 
    {     0.00000001348,  5.54306182308,      625.67019231240}, 
    {     0.00000000964,  5.49710119494,      853.19638175200}, 
    {     0.00000000947,  2.34829918409,      639.89728631400}, 
    {     0.00000000798,  3.37909370240,      220.41264243880}, 
    {     0.00000000707,  1.57787722219,     1692.16566950240}, 
    {     0.00000000591,  0.29761569203,      213.29909543800}, 
    {     0.00000000572,  1.28691054813,      508.35032409220}, 
    {     0.00000000512,  2.56537612741,     1265.56747862640}, 
    {     0.00000000665,  6.11880936688,      728.76296653100}, 
    {     0.00000000447,  4.60869261113,     2125.87740737920}, 
    {     0.00000000586,  4.43282799664,      330.61896365820}, 
    {     0.00000000414,  1.25349133607,     1258.45393162560}, 
    {     0.00000000524,  2.96141918447,     2648.45482547300}, 
    {     0.00000000444,  3.19923402818,     1062.56332392690}, 
    {     0.00000000404,  1.79288519616,     1485.98012106520}, 
    {     0.00000000375,  0.79587902858,      838.96928775040}, 
    {     0.00000000353,  3.34547139217,      199.07200143640}, 
    {     0.00000000452,  5.08983741758,      846.08283475120}, 
    {     0.00000000334,  3.04324482994,      551.03160609700}, 
    {     0.00000000366,  1.68895713870,      519.39602435610}, 
    {     0.00000000394,  1.57570736696,      412.37109687440}, 
    {     0.00000000301,  3.37032774636,      309.27832265580}, 
    {     0.00000000291,  2.62531230776,      539.98590583310}, 
    {     0.00000000325,  0.15647873172,     1574.84580128220}, 
    {     0.00000000245,  3.25292367144,     1272.68102562720}, 
    {     0.00000000217,  3.11492452322,     1699.27921650320}, 
    {     0.00000000184,  1.08716393617,     1478.86657406440}, 
    {     0.00000000148,  2.68589605205,      440.82528487760}, 
    {     0.00000000151,  3.55666552483,      227.52618943960}, 
    {     0.00000000159,  4.59287441360,        3.18139373770}, 
    {     0.00000000136,  4.84859091336,     1375.77379984580}, 
    {     0.00000000163,  2.32840480908,     1368.66025284500}, 
    {     0.00000000143,  3.22177095400,     1055.44977692610}, 
    {     0.00000000142,  5.72788361902,     1471.75302706360}, 
    {     0.00000000158,  4.73812763868,       21.34064100240}, 
    {     0.00000000128,  2.70021949677,      742.99006053260}, 
    {     0.00000000139,  1.17163391807,     1056.20053645150}, 
    {     0.00000000145,  0.86475461158,     2111.65031337760}, 
    {     0.00000000113,  0.93475856540,     1685.05212250160}, 
    {     0.00000000092,  6.08486890659,     1038.04128918680}, 
    {     0.00000000077,  1.76503406298,     1795.25844372100}, 
    {     0.00000000076,  1.81177242528,     2221.85663459700}, 
    {     0.00000000077,  3.87925580596,     1603.29998928540}, 
};


static const struct ln_vsop jupiter_latitude_b3[LAT_B3] = {
    {     0.00000185332,  4.79276761490,      529.69096509460}, 
    {     0.00000085668,  1.40023038638,      536.80451209540}, 
    {     0.00000056359,  2.81574766965,      522.57741809380}, 
    {     0.00000019435,  6.25741008684,     1059.38193018920}, 
    {     0.00000010858,  2.04333735353,     1066.49547719000}, 
    {     0.00000014477,  0.00000000000,        0.00000000000}, 
    {     0.00000005535,  2.75732372347,      515.46387109300}, 
    {     0.00000004939,  1.29727834284,      543.91805909620}, 
    {     0.00000004970,  2.56009290021,     1052.26838318840}, 
    {     0.00000004112,  0.86840480428,     1589.07289528380}, 
    {     0.00000003798,  2.86619114773,        7.11354700080}, 
    {     0.00000001107,  2.66033381472,     1596.18644228460}, 
    {     0.00000001093,  1.82485496219,     1045.15483618760}, 
    {     0.00000001031,  2.82866669066,       14.22709400160}, 
    {     0.00000000433,  4.07064796547,      419.48464387520}, 
    {     0.00000000441,  1.38849268510,     2118.76386037840}, 
    {     0.00000000427,  1.88306006605,     1073.60902419080}, 
    {     0.00000000385,  3.43063155260,      110.20632121940}, 
    {     0.00000000270,  0.28254340737,      942.06206196900}, 
    {     0.00000000282,  2.56588914137,      323.50541665740}, 
    {     0.00000000281,  1.78450485408,      735.87651353180}, 
    {     0.00000000250,  3.01246535740,      508.35032409220}, 
    {     0.00000000218,  2.72492160401,     1581.95934828300}, 
    {     0.00000000210,  0.07248270409,      632.78373931320}, 
    {     0.00000000225,  3.97044557000,      117.31986822020}, 
    {     0.00000000203,  0.07858321388,      639.89728631400}, 
    {     0.00000000170,  0.89620998933,     1169.58825140860}, 
    {     0.00000000165,  1.56025270981,      625.67019231240}, 
    {     0.00000000156,  5.58460103668,      103.09277421860}, 
    {     0.00000000137,  4.26368918979,       95.97922721780}, 
    {     0.00000000100,  1.72309553591,      949.17560896980}, 
    {     0.00000000094,  2.26854098455,     1155.36115740700}, 
    {     0.00000000082,  5.02874146441,      956.28915597060}, 
};


static const struct ln_vsop jupiter_latitude_b4[LAT_B4] = {
    {     0.00000008963,  5.93887232380,      536.80451209540}, 
    {     0.00000005280,  4.80778878768,      522.57741809380}, 
    {     0.00000001161,  0.46295890438,     1066.49547719000}, 
    {     0.00000001104,  4.53240452495,      515.46387109300}, 
    {     0.00000001087,  5.81789252627,      543.91805909620}, 
    {     0.00000000818,  1.49293156118,      529.69096509460}, 
    {     0.00000000595,  4.58881648484,     1059.38193018920}, 
    {     0.00000000513,  4.57214361679,     1052.26838318840}, 
    {     0.00000000179,  0.75821264280,        7.11354700080}, 
    {     0.00000000143,  5.78292264064,     1589.07289528380}, 
    {     0.00000000135,  1.57382028639,       14.22709400160}, 
    {     0.00000000096,  1.04662476547,     1596.18644228460}, 
    {     0.00000000077,  3.58780641570,     1045.15483618760}, 
};


static const struct ln_vsop jupiter_latitude_b5[LAT_B5] = {
    {     0.00000000662,  4.10413626462,      536.80451209540}, 
    {     0.00000000431,  0.82614663721,      522.57741809380}, 
    {     0.00000000208,  0.05498457769,      515.46387109300}, 
};


static const struct ln_vsop jupiter_radius_r0[RADIUS_R0] = {
    {     5.20887429326,  0.00000000000,        0.00000000000}, 
    {     0.25209327119,  3.49108639871,      529.69096509460}, 
    {     0.00610599976,  3.84115365948,     1059.38193018920}, 
    {     0.00282029458,  2.57419881293,      632.78373931320}, 
    {     0.00187647346,  2.07590383214,      522.57741809380}, 
    {     0.00086792905,  0.71001145545,      419.48464387520}, 
    {     0.00072062974,  0.21465724607,      536.80451209540}, 
    {     0.00065517248,  5.97995884790,      316.39186965660}, 
    {     0.00029134542,  1.67759379655,      103.09277421860}, 
    {     0.00030135335,  2.16132003734,      949.17560896980}, 
    {     0.00023453271,  3.54023522184,      735.87651353180}, 
    {     0.00022283743,  4.19362594399,     1589.07289528380}, 
    {     0.00023947298,  0.27458037480,        7.11354700080}, 
    {     0.00013032614,  2.96042965363,     1162.47470440780}, 
    {     0.00009703360,  1.90669633585,      206.18554843720}, 
    {     0.00012749023,  2.71550286592,     1052.26838318840}, 
    {     0.00009161393,  4.41352953117,      213.29909543800}, 
    {     0.00007894511,  2.47907592482,      426.59819087600}, 
    {     0.00007057931,  2.18184839926,     1265.56747862640}, 
    {     0.00006137703,  6.26418240033,      846.08283475120}, 
    {     0.00005477001,  5.65729989857,      639.89728631400}, 
    {     0.00003502493,  0.56532365822,     1066.49547719000}, 
    {     0.00004136822,  2.72220872400,      625.67019231240}, 
    {     0.00004169954,  2.01603822251,      515.46387109300}, 
    {     0.00002499967,  4.55181655381,      838.96928775040}, 
    {     0.00002616976,  2.00994012876,     1581.95934828300}, 
    {     0.00001912009,  0.85621128851,      412.37109687440}, 
    {     0.00002127681,  6.12755221002,      742.99006053260}, 
    {     0.00001610567,  3.08871452594,     1368.66025284500}, 
    {     0.00001479513,  2.68021307468,     1478.86657406440}, 
    {     0.00001230630,  1.89052048109,      323.50541665740}, 
    {     0.00001216895,  1.80176263029,      110.20632121940}, 
    {     0.00000961113,  4.54876995367,     2118.76386037840}, 
    {     0.00000885764,  4.14783869943,      533.62311835770}, 
    {     0.00000776583,  3.67710828843,      728.76296653100}, 
    {     0.00000998591,  2.87205397992,      309.27832265580}, 
    {     0.00001014733,  1.38675822271,      454.90936652730}, 
    {     0.00000727156,  3.98827252563,     1155.36115740700}, 
    {     0.00000655334,  2.79072596910,     1685.05212250160}, 
    {     0.00000821383,  1.59351544602,     1898.35121793960}, 
    {     0.00000620818,  4.82275194351,      956.28915597060}, 
    {     0.00000654071,  3.38140746852,     1692.16566950240}, 
    {     0.00000811993,  5.94093410097,      909.81873305460}, 
    {     0.00000562092,  0.08114877791,      543.91805909620}, 
    {     0.00000542222,  0.28357235311,      525.75881183150}, 
    {     0.00000457841,  0.12720499202,     1375.77379984580}, 
    {     0.00000614740,  2.27633681284,      942.06206196900}, 
    {     0.00000435816,  2.60279250213,       95.97922721780}, 
    {     0.00000496009,  5.53020241869,      380.12776796000}, 
    {     0.00000469974,  2.81883756859,     1795.25844372100}, 
    {     0.00000445057,  0.14648640292,       14.22709400160}, 
    {     0.00000290917,  3.89373030829,     1471.75302706360}, 
    {     0.00000276581,  2.52188912681,     2001.44399215820}, 
    {     0.00000275010,  2.98827073289,      526.50957135690}, 
    {     0.00000293746,  2.04945754349,      199.07200143640}, 
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    {     0.00000000542,  3.28894870834,    10103.07922499160}, 
    {     0.00000000544,  0.69476773349,     4642.78527063040}, 
    {     0.00000000564,  0.72677136462,     1059.22187149480}, 
    {     0.00000000546,  0.45425690852,     4694.00295470760}, 
    {     0.00000000585,  2.82650088707,      344.70304530790}, 
    {     0.00000000528,  2.32101188937,      949.22379307960}, 
    {     0.00000000530,  4.99510636441,     9264.10993724120}, 
    {     0.00000000567,  5.13926871155,      288.08069400530}, 
    {     0.00000000527,  5.40641191628,      949.12742486000}, 
    {     0.00000000531,  0.16792029802,     1080.72257119160}, 
    {     0.00000000535,  1.42855602314,        9.56122755560}, 
    {     0.00000000688,  0.46353180630,      842.15068148810}, 
    {     0.00000000697,  4.99042365686,       12.53017297220}, 
    {     0.00000000553,  5.23792586314,      528.04643369190}, 
    {     0.00000000504,  2.58550284000,     5378.66178416220}, 
    {     0.00000000519,  3.10157097770,     9161.01716302260}, 
    {     0.00000000619,  3.71554817226,     2090.30967237520}, 
    {     0.00000000621,  3.98893673383,      409.92341631960}, 
    {     0.00000000544,  1.05857942311,     1438.02522544090}, 
    {     0.00000000541,  3.07978704943,     1446.62324515000}, 
    {     0.00000000488,  5.26894402637,     1751.53953141600}, 
    {     0.00000000639,  2.98874052475,     2349.32843120380}, 
    {     0.00000000684,  2.97458993261,      298.23262239190}, 
    {     0.00000000555,  3.57205235856,     1144.31545714310}, 
    {     0.00000000482,  1.84410406707,     1077.54117745390}, 
    {     0.00000000493,  2.66756696257,      849.26422848890}, 
    {     0.00000000553,  5.31312350142,      531.33549649730}, 
    {     0.00000000612,  1.26746376254,      878.32616366560}, 
    {     0.00000000581,  5.77185453327,      745.43774108740}, 
    {     0.00000000537,  3.67807254097,      605.95703637020}, 
    {     0.00000000476,  3.28733354824,      734.91330568530}, 
    {     0.00000000493,  3.73487080434,      131.40394986990}, 
    {     0.00000000493,  1.24342391046,    11506.76976979360}, 
    {     0.00000000613,  3.84144928692,     1065.01100448170}, 
    {     0.00000000579,  0.02333971761,     1069.67687092770}, 
    {     0.00000000653,  2.40326963363,      657.16276170140}, 
    {     0.00000000509,  0.70662672351,     1570.91364801910}, 
    {     0.00000000564,  3.81960833918,     1059.54198888360}, 
    {     0.00000000468,  3.50348554992,     4841.85727206680}, 
    {     0.00000000621,  4.58816416137,      105.54045477340}, 
    {     0.00000000592,  0.99424149467,      920.86443331850}, 
    {     0.00000000457,  2.38193571955,      990.22940591440}, 
    {     0.00000000458,  5.94092303682,      513.22863885930}, 
    {     0.00000000462,  1.09795189347,      100.17201291180}, 
    {     0.00000000491,  1.28733237388,      247.23934538180}, 
    {     0.00000000473,  5.02679239007,      103.04459010880}, 
    {     0.00000000540,  0.54791737146,    51646.11531805379}, 
    {     0.00000000531,  0.30026207053,      912.78767847120}, 
    {     0.00000000488,  5.32348416682,     1432.39615114840}, 
    {     0.00000000449,  3.02583472996,     5901.23920225600}, 
    {     0.00000000543,  2.98751942458,     4223.30062675520}, 
    {     0.00000000629,  2.75622390887,      334.55111692130}, 
    {     0.00000000481,  3.63292807076,     5584.84733259940}, 
    {     0.00000000444,  4.61008831817,      546.15329132990}, 
    {     0.00000000622,  2.29597570837,     9999.98645077300}, 
    {     0.00000000588,  5.46780291871,      668.20846196530}, 
    {     0.00000000485,  0.74674429026,      736.83972137830}, 
    {     0.00000000595,  3.78181802412,     6386.16862421000}, 
    {     0.00000000567,  0.38348819779,      737.36098624010}, 
    {     0.00000000474,  3.37296965859,     3803.81598288000}, 
    {     0.00000000434,  2.64411689486,      748.40668650400}, 
    {     0.00000000604,  0.87482329646,     6069.77675455340}, 
    {     0.00000000520,  2.12596982279,      906.84978763800}, 
    {     0.00000000513,  5.10763567804,     1090.40141882620}, 
    {     0.00000000459,  4.06923787133,     5216.58037280140}, 
    {     0.00000000466,  2.29198238542,     2225.78878786010}, 
    {     0.00000000589,  0.74050145875,     1291.43097372290}, 
    {     0.00000000466,  2.43707405011,     3362.99069800240}, 
    {     0.00000000566,  0.59740900184,      350.33211960040}, 
    {     0.00000000429,  2.46364296538,     3914.02230409940}, 
    {     0.00000000474,  5.19232279677,      857.12853501510}, 
    {     0.00000000429,  0.59245436963,     1065.60170531270}, 
    {     0.00000000511,  2.44662587368,     9690.70812811720}, 
    {     0.00000000424,  1.67088834417,      148.07872442630}, 
    {     0.00000000412,  3.29630633921,        7.32599532190}, 
    {     0.00000000436,  1.40801830895,      995.64603188580}, 
    {     0.00000000429,  2.13901349243,     3473.19701922180}, 
    {     0.00000000510,  4.29090556636,     2545.36205125440}, 
    {     0.00000000501,  5.84167833830,     9676.48103411560}, 
    {     0.00000000548,  6.03429743373,     9367.20271145980}, 
    {     0.00000000433,  0.43309624811,      735.82832942200}, 
    {     0.00000000433,  5.93397926660,     1688.23351623930}, 
    {     0.00000000429,  2.18700390627,     1357.61455258110}, 
    {     0.00000000439,  0.44871247921,      512.42548970720}, 
    {     0.00000000555,  1.00328633116,      141.22580985640}, 
    {     0.00000000441,  3.06678924251,     1475.68518032670}, 
    {     0.00000000544,  2.22925308079,     1440.99417085750}, 
    {     0.00000000404,  3.51410520211,     1329.30337692980}, 
    {     0.00000000412,  5.87495245826,        6.90109867970}, 
    {     0.00000000442,  5.37772982571,      104.05598206510}, 
    {     0.00000000465,  1.93436756934,     6275.96230299060}, 
    {     0.00000000401,  2.90426785776,     1987.21689815660}, 
    {     0.00000000481,  6.21043578332,      683.98946464440}, 
    {     0.00000000385,  0.13151986614,      970.51624997220}, 
    {     0.00000000383,  6.02073818555,     1268.74887236410}, 
    {     0.00000000391,  2.81753436573,     5798.14642803740}, 
    {     0.00000000395,  0.22367886581,    51116.42435295920}, 
    {     0.00000000480,  3.89516556182,      967.33485623450}, 
    {     0.00000000426,  3.81910977181,      546.95644048200}, 
    {     0.00000000471,  6.24506463249,      946.46729598410}, 
    {     0.00000000379,  1.14527123185,     1059.59437851030}, 
    {     0.00000000371,  6.15750793727,      509.24409596950}, 
    {     0.00000000476,  4.40755251309,     2200.51599359460}, 
    {     0.00000000511,  5.53118344106,     1128.53445446400}, 
};


static const struct ln_vsop jupiter_radius_r1[RADIUS_R1] = {
    {     0.01271801520,  2.64937512894,      529.69096509460}, 
    {     0.00061661816,  3.00076460387,     1059.38193018920}, 
    {     0.00053443713,  3.89717383175,      522.57741809380}, 
    {     0.00031185171,  4.88276958012,      536.80451209540}, 
    {     0.00041390269,  0.00000000000,        0.00000000000}, 
    {     0.00011847263,  2.41328764459,      419.48464387520}, 
    {     0.00009166454,  4.75978553741,        7.11354700080}, 
    {     0.00003175595,  2.79298354393,      103.09277421860}, 
    {     0.00003203481,  5.21084121495,      735.87651353180}, 
    {     0.00003403577,  3.34689633223,     1589.07289528380}, 
    {     0.00002599925,  3.63439058628,      206.18554843720}, 
    {     0.00002412127,  1.46948314626,      426.59819087600}, 
    {     0.00002806070,  3.74227009702,      515.46387109300}, 
    {     0.00002676611,  4.33051702874,     1052.26838318840}, 
    {     0.00002100392,  3.92772817188,      639.89728631400}, 
    {     0.00001646160,  5.30947626153,     1066.49547719000}, 
    {     0.00001641093,  4.41628521235,      625.67019231240}, 
    {     0.00001049766,  3.16115576687,      213.29909543800}, 
    {     0.00001024703,  2.55437897122,      412.37109687440}, 
    {     0.00000740834,  2.17089042827,     1162.47470440780}, 
    {     0.00000806430,  2.67747285932,      632.78373931320}, 
    {     0.00000676729,  6.24979690660,      838.96928775040}, 
    {     0.00000468918,  4.70985711091,      543.91805909620}, 
    {     0.00000444628,  0.40306241278,      323.50541665740}, 
    {     0.00000567074,  4.57671527249,      742.99006053260}, 
    {     0.00000415840,  5.36847472493,      728.76296653100}, 
    {     0.00000484810,  2.46907968946,      949.17560896980}, 
    {     0.00000337576,  3.16751996354,      956.28915597060}, 
    {     0.00000401711,  4.60509281258,      309.27832265580}, 
    {     0.00000347330,  4.68154619204,       14.22709400160}, 
    {     0.00000260727,  5.34286862943,      846.08283475120}, 
    {     0.00000220020,  4.84195212656,     1368.66025284500}, 
    {     0.00000203233,  5.60019394971,     1155.36115740700}, 
    {     0.00000246438,  3.92373109496,      942.06206196900}, 
    {     0.00000183575,  4.26454732757,       95.97922721780}, 
    {     0.00000197119,  3.70582665656,     2118.76386037840}, 
    {     0.00000179982,  4.40213614840,      532.87235883230}, 
    {     0.00000195844,  3.75886519686,      199.07200143640}, 
    {     0.00000200140,  4.43930806722,     1045.15483618760}, 
    {     0.00000170248,  4.84663902529,      526.50957135690}, 
    {     0.00000146328,  6.12953407685,      533.62311835770}, 
    {     0.00000133441,  1.32112984738,      110.20632121940}, 
    {     0.00000132030,  4.51111768540,      525.75881183150}, 
    {     0.00000123776,  2.04233591660,     1478.86657406440}, 
    {     0.00000121876,  4.40555373903,     1169.58825140860}, 
    {     0.00000115354,  4.46752336410,     1581.95934828300}, 
    {     0.00000098559,  5.72824115387,     1596.18644228460}, 
    {     0.00000091744,  4.53147949989,     1685.05212250160}, 
    {     0.00000110685,  3.62539004538,     1272.68102562720}, 
    {     0.00000080515,  4.11374100758,     1258.45393162560}, 
    {     0.00000079518,  2.71923662078,     1692.16566950240}, 
    {     0.00000100157,  5.24639992412,     1265.56747862640}, 
    {     0.00000077866,  5.56575552496,     1471.75302706360}, 
    {     0.00000085840,  0.07984103333,      831.85574074960}, 
    {     0.00000082132,  3.80763065130,      508.35032409220}, 
    {     0.00000055296,  0.35136399335,      316.39186965660}, 
    {     0.00000052289,  5.53069765044,      433.71173787680}, 
    {     0.00000055809,  4.75224156118,      302.16477565500}, 
    {     0.00000050625,  4.85603624371,     1375.77379984580}, 
    {     0.00000043539,  4.94471526157,     1361.54670584420}, 
    {     0.00000042146,  1.22819828957,      853.19638175200}, 
    {     0.00000037653,  4.26849585975,     2001.44399215820}, 
    {     0.00000049301,  4.01704532497,      220.41264243880}, 
    {     0.00000038248,  5.33256180883,     1788.14489672020}, 
    {     0.00000035653,  1.76300235040,     1795.25844372100}, 
    {     0.00000036185,  3.85316960087,     1574.84580128220}, 
    {     0.00000029178,  5.16817654180,        3.93215326310}, 
    {     0.00000025113,  4.33889766890,      519.39602435610}, 
    {     0.00000024766,  2.72782261862,      405.25754987360}, 
    {     0.00000027102,  6.09843304423,     1148.24761040620}, 
    {     0.00000022665,  0.19350039559,      380.12776796000}, 
    {     0.00000020538,  4.32862762591,        3.18139373770}, 
    {     0.00000019941,  4.63435849910,     1677.93857550080}, 
    {     0.00000019522,  5.10728297130,     1073.60902419080}, 
    {     0.00000018500,  3.76514376541,     1485.98012106520}, 
    {     0.00000018845,  5.05703372830,     2104.53676637680}, 
    {     0.00000016987,  4.02069213446,     2317.83586181480}, 
    {     0.00000016680,  5.43302879610,       88.86568021700}, 
    {     0.00000015372,  2.91841323048,     2008.55753915900}, 
    {     0.00000014419,  3.63960739927,      628.85158605010}, 
    {     0.00000014630,  5.51305730294,      721.64941953020}, 
    {     0.00000018540,  6.02594081104,      330.61896365820}, 
    {     0.00000013638,  4.88575627207,      629.60234557550}, 
    {     0.00000013472,  1.38742780013,      518.64526483070}, 
    {     0.00000015538,  2.93208280366,     1905.46476494040}, 
    {     0.00000012405,  1.58727793866,     2111.65031337760}, 
    {     0.00000012168,  3.37798229468,      635.96513305090}, 
    {     0.00000011835,  4.08484570984,     2648.45482547300}, 
    {     0.00000011259,  4.62303293007,      636.71589257630}, 
    {     0.00000014286,  2.74041502983,     2221.85663459700}, 
    {     0.00000011157,  3.54867395941,     1891.23767093880}, 
    {     0.00000013131,  5.83476507713,     1464.63948006280}, 
    {     0.00000011346,  2.57830184286,      511.53171782990}, 
    {     0.00000010484,  0.49631744855,      453.42489381900}, 
    {     0.00000009712,  4.39039807014,     1994.33044515740}, 
    {     0.00000010072,  2.75854126409,      423.41679713830}, 
    {     0.00000008973,  4.79620568259,     2420.92863603340}, 
    {     0.00000008487,  5.15862241737,     1056.20053645150}, 
    {     0.00000008037,  3.72684449392,     2634.22773147140}, 
    {     0.00000008036,  1.28481352995,     2428.04218303420}, 
    {     0.00000008823,  1.84296748834,      750.10360753340}, 
    {     0.00000008976,  4.81284969227,     1062.56332392690}, 
    {     0.00000008608,  4.53451403086,       21.34064100240}, 
    {     0.00000009412,  4.34166457358,     1802.37199072180}, 
    {     0.00000006904,  5.96626034536,      540.73666535850}, 
    {     0.00000007268,  4.98087083693,     1699.27921650320}, 
    {     0.00000007068,  4.99227057771,     1055.44977692610}, 
    {     0.00000007244,  4.97266787687,     1898.35121793960}, 
    {     0.00000006479,  1.40223433818,      422.66603761290}, 
    {     0.00000006280,  3.64802738608,      621.73803904930}, 
    {     0.00000006231,  4.45749513375,      551.03160609700}, 
    {     0.00000006271,  6.13813110445,     2125.87740737920}, 
    {     0.00000006801,  2.92013819097,     2324.94940881560}, 
    {     0.00000005898,  2.58873003212,      569.04784100980}, 
    {     0.00000006481,  4.58107849781,     1038.04128918680}, 
    {     0.00000006653,  5.54500062883,     1781.03134971940}, 
    {     0.00000007187,  3.02482572051,      416.30325013750}, 
    {     0.00000005141,  6.21519498122,      963.40270297140}, 
    {     0.00000005878,  4.23185657623,      539.98590583310}, 
    {     0.00000005119,  0.06958852255,     1063.31408345230}, 
    {     0.00000005247,  0.16792912472,      117.31986822020}, 
    {     0.00000005423,  4.93524030417,      835.03713448730}, 
    {     0.00000006217,  3.87980766892,      191.95845443560}, 
    {     0.00000004967,  1.34452103048,     1382.88734684660}, 
    {     0.00000004635,  4.63642027299,      643.82943957710}, 
    {     0.00000004561,  3.37093181163,     2207.62954059540}, 
    {     0.00000004474,  4.07436890901,     2310.72231481400}, 
    {     0.00000004703,  4.55179426438,     2737.32050569000}, 
    {     0.00000004487,  1.48312334127,      408.43894361130}, 
    {     0.00000004087,  1.12906821675,      415.55249061210}, 
    {     0.00000005489,  5.62261637529,      618.55664531160}, 
    {     0.00000004323,  4.60454457547,      647.01083331480}, 
    {     0.00000003882,  4.09352825462,      430.53034413910}, 
    {     0.00000003747,  3.41170997719,     2950.61960112800}, 
    {     0.00000003803,  2.19632996017,      534.35683154060}, 
    {     0.00000003634,  1.03495466077,     2744.43405269080}, 
    {     0.00000004549,  4.21325324482,      227.52618943960}, 
    {     0.00000003565,  4.11240029730,      440.82528487760}, 
    {     0.00000003852,  1.14937815780,       74.78159856730}, 
    {     0.00000003525,  4.27662025409,       10.29494073850}, 
    {     0.00000003488,  5.33792561596,      458.84151979040}, 
    {     0.00000004208,  2.38049728614,     2538.24850425360}, 
    {     0.00000004465,  0.18617267547,      824.74219374880}, 
    {     0.00000003327,  5.51323389248,      739.80866679490}, 
    {     0.00000003252,  2.68329422796,      561.93429400900}, 
    {     0.00000003247,  4.88392621669,      295.05122865420}, 
    {     0.00000003571,  4.64017933384,     2214.74308759620}, 
    {     0.00000003469,  4.34266924360,      305.34616939270}, 
    {     0.00000003430,  3.34792668508,      149.56319713460}, 
    {     0.00000003474,  2.75054677372,     2641.34127847220}, 
    {     0.00000003618,  5.30205670433,     2097.42321937600}, 
    {     0.00000002963,  1.32779700914,      611.44309831080}, 
    {     0.00000002826,  0.91971516521,      984.60033162190}, 
    {     0.00000003445,  1.63289286159,      525.02509864860}, 
    {     0.00000002635,  5.25522783247,      532.13864564940}, 
    {     0.00000002682,  4.24680441193,     3053.71237534660}, 
    {     0.00000002655,  3.18365951037,      527.24328453980}, 
    {     0.00000002418,  4.23791881124,      217.23124870110}, 
    {     0.00000002231,  4.23923472684,      739.05790726950}, 
    {     0.00000002268,  5.52248110560,      524.27433912320}, 
    {     0.00000002095,  4.85943251945,     1049.08698945070}, 
    {     0.00000002054,  5.38759557118,      142.44965013380}, 
    {     0.00000002058,  3.79500539044,     2627.11418447060}, 
    {     0.00000002536,  3.95352520357,      210.11770170030}, 
    {     0.00000002095,  5.76269812349,      529.64278098480}, 
    {     0.00000002533,  5.82849252925,      732.69511979410}, 
    {     0.00000002025,  4.20638434497,      945.99421523210}, 
    {     0.00000002248,  1.61218306133,      604.47256366190}, 
    {     0.00000001923,  4.75088270631,      535.10759106600}, 
    {     0.00000001969,  5.49257949498,     1439.50969814920}, 
    {     0.00000001876,  3.26958300763,     3267.01147078460}, 
    {     0.00000002286,  2.93860898500,       76.26607127560}, 
    {     0.00000002298,  2.67602302579,      760.25553592000}, 
    {     0.00000002074,  5.85386852879,      532.61172640140}, 
    {     0.00000002160,  3.89934769002,     2435.15573003500}, 
    {     0.00000001763,  3.18823524810,     2524.02141025200}, 
    {     0.00000001681,  0.78838681637,     3060.82592234740}, 
    {     0.00000002121,  0.41035912497,     1279.79457262800}, 
    {     0.00000001660,  2.34370903423,      528.72775724810}, 
    {     0.00000001642,  4.07579944140,      731.94436026870}, 
    {     0.00000002095,  2.67732367556,      529.73914920440}, 
    {     0.00000001712,  4.29334392085,      724.83081326790}, 
    {     0.00000001856,  2.76989081814,      952.35700270750}, 
    {     0.00000001904,  2.48369702447,     2957.73314812880}, 
    {     0.00000002003,  5.04729621715,     2413.81508903260}, 
    {     0.00000001672,  0.28599461931,      454.90936652730}, 
    {     0.00000001582,  5.84371262844,      547.85021235930}, 
    {     0.00000001595,  1.18530166527,       38.13303563780}, 
    {     0.00000001563,  3.02970693113,      945.24345570670}, 
    {     0.00000001542,  1.12520322838,     1021.24889455140}, 
    {     0.00000001546,  0.38348247678,      319.57326339430}, 
    {     0.00000001463,  0.61055082613,      312.45971639350}, 
    {     0.00000001604,  3.50041190037,      934.94851496820}, 
    {     0.00000001439,  4.26513521887,      526.77020378780}, 
    {     0.00000001611,  5.24344469844,     1354.43315884340}, 
    {     0.00000001511,  5.49591876170,       81.75213321620}, 
    {     0.00000001906,  3.78137493812,      953.10776223290}, 
    {     0.00000001656,  6.09667089740,      530.65417294110}, 
    {     0.00000001799,  5.83566265631,      909.81873305460}, 
    {     0.00000001405,  4.32629307157,     3178.14579056760}, 
    {     0.00000001406,  4.05527527402,     1158.54255114470}, 
    {     0.00000001493,  3.29690433844,     1041.22268292450}, 
    {     0.00000001558,  1.51646768353,      902.70518605380}, 
    {     0.00000001387,  2.52840497309,      530.44172462000}, 
    {     0.00000001410,  0.07169032313,      490.33408917940}, 
    {     0.00000001562,  1.86268966974,      437.64389113990}, 
    {     0.00000001606,  4.27835003095,     2531.13495725280}, 
    {     0.00000001794,  6.21722587878,       18.15924726470}, 
    {     0.00000001422,  3.98206620893,     3370.10424500320}, 
    {     0.00000001515,  0.17967750365,     1141.13406340540}, 
    {     0.00000001329,  5.84479773498,      387.24131496080}, 
    {     0.00000001300,  0.29821177492,      597.35901666110}, 
    {     0.00000001710,  2.23503932366,     2854.64037391020}, 
    {     0.00000001558,  6.17783174275,      983.11585891360}, 
    {     0.00000001311,  3.75085875476,     1165.65609814550}, 
    {     0.00000001482,  0.83066678204,      529.16970023280}, 
    {     0.00000001435,  0.23355762296,      860.30992875280}, 
    {     0.00000001141,  3.46612877999,      483.22054217860}, 
    {     0.00000001133,  2.81368303631,      124.43341522100}, 
    {     0.00000001319,  4.88148483038,     1251.34038462480}, 
    {     0.00000001508,  3.48139955389,     2751.54759969160}, 
    {     0.00000001237,  0.90332265294,      916.93228005540}, 
    {     0.00000001142,  5.61457234897,      337.73251065900}, 
    {     0.00000001076,  5.49947769870,     1585.89150154610}, 
    {     0.00000001123,  1.45270581179,      533.88375078860}, 
    {     0.00000001067,  5.29710936450,     1159.29331067010}, 
    {     0.00000001063,  3.52724300315,     2943.50605412720}, 
    {     0.00000001416,  5.18377634152,     1592.25428902150}, 
    {     0.00000001054,  1.67751055664,      497.44763618020}, 
    {     0.00000001338,  3.48243389264,      107.02492748170}, 
    {     0.00000001037,  3.12801094422,       70.84944530420}, 
    {     0.00000001102,  4.18000348718,      203.00415469950}, 
    {     0.00000001021,  5.62851625196,     1603.29998928540}, 
    {     0.00000000967,  2.80222742968,     3583.40334044120}, 
    {     0.00000001106,  4.86492659899,     1166.40685767090}, 
    {     0.00000001093,  3.23230823003,      447.79581952650}, 
    {     0.00000001073,  0.35668643110,     1593.00504854690}, 
    {     0.00000001108,  2.42061915107,      106.27416795630}, 
    {     0.00000001003,  3.80070721725,       99.91138048090}, 
    {     0.00000000987,  2.44184933100,     1048.33622992530}, 
    {     0.00000000921,  0.12955317257,     1070.42763045310}, 
    {     0.00000001136,  2.26568590950,      525.49817940060}, 
    {     0.00000000885,  4.25304247204,      114.13847448250}, 
    {     0.00000001168,  2.68377982079,      209.36694217490}, 
    {     0.00000000967,  4.47667348232,     9676.48103411560}, 
    {     0.00000000875,  0.22303452734,      460.53844081980}, 
    {     0.00000001067,  4.72721946609,     2730.20695868920}, 
    {     0.00000001165,  1.56030440737,      630.33605875840}, 
    {     0.00000000951,  0.49347419163,      842.90144101350}, 
    {     0.00000000884,  4.75139536245,      960.22130923370}, 
    {     0.00000001158,  5.50047449313,      224.34479570190}, 
    {     0.00000000892,  2.26616982044,      327.43756992050}, 
    {     0.00000000940,  0.06481852204,      746.92221379570}, 
    {     0.00000000899,  1.78944295718,        4.66586644600}, 
    {     0.00000000894,  3.06608347131,     5746.27133789600}, 
    {     0.00000000936,  5.35932787694,     1585.14074202070}, 
    {     0.00000000866,  1.40863222239,      202.25339517410}, 
    {     0.00000000865,  2.85348523795,      938.12990870590}, 
    {     0.00000000782,  0.49776082272,     3377.21779200400}, 
    {     0.00000000822,  4.08331963114,      501.23677709140}, 
    {     0.00000000933,  0.30976125598,      685.47393735270}, 
    {     0.00000001033,  2.47031686819,     3274.12501778540}, 
    {     0.00000000799,  2.08457026425,    77734.01845962799}, 
    {     0.00000001017,  5.24406833089,      842.15068148810}, 
    {     0.00000000741,  1.32379374647,      530.21222995640}, 
    {     0.00000000842,  3.39449778904,      484.44438245600}, 
    {     0.00000000821,  0.48415264993,      850.01498801430}, 
    {     0.00000000825,  3.48499388498,      498.67147645760}, 
    {     0.00000000781,  1.03963400654,      373.01422095920}, 
    {     0.00000000759,  3.82014111206,     6283.07584999140}, 
    {     0.00000000915,  2.89101498678,      462.02291352810}, 
    {     0.00000000770,  0.27005681805,     2655.56837247380}, 
    {     0.00000000707,  5.77702928333,      429.77958461370}, 
    {     0.00000000862,  5.01184578153,     1567.73225428140}, 
    {     0.00000000711,  4.82250918143,       11.77941344680}, 
    {     0.00000000692,  2.63705354662,        6.59228213900}, 
    {     0.00000000771,  3.87410612014,     9690.70812811720}, 
    {     0.00000000668,  1.79396450309,      775.23338944700}, 
    {     0.00000000740,  3.39423131656,       99.16062095550}, 
    {     0.00000000663,  5.27704405712,     4532.57894941100}, 
    {     0.00000000759,  5.45358686570,     9683.59458111640}, 
    {     0.00000000709,  3.71117647887,     3686.49611465980}, 
    {     0.00000000677,  4.27891183416,    25028.52121138500}, 
    {     0.00000000784,  5.33244311918,      827.92358748650}, 
    {     0.00000000664,  6.08614002142,     2281.23049651060}, 
    {     0.00000000643,  1.40239510103,     9161.01716302260}, 
    {     0.00000000656,  0.60909845504,      835.78789401270}, 
    {     0.00000000702,  6.10412979847,     4635.67172362960}, 
    {     0.00000000809,  4.19626489638,     5753.38488489680}, 
    {     0.00000000700,  4.95131303046,     1670.82502850000}, 
    {     0.00000000838,  4.51443146541,     1069.67687092770}, 
    {     0.00000000626,  4.38443691624,        5.41662597140}, 
    {     0.00000000700,  3.78143557545,     2818.03500860600}, 
    {     0.00000000701,  4.28283847329,     2803.80791460440}, 
    {     0.00000000729,  4.62695452187,     2228.97018159780}, 
    {     0.00000000604,  3.05855704532,     2840.41327990860}, 
    {     0.00000000678,  2.45013730979,     5760.49843189760}, 
    {     0.00000000624,  0.61517599566,     1176.70179840940}, 
    {     0.00000000717,  1.82600293291,     3171.03224356680}, 
    {     0.00000000617,  5.74358811142,     1061.82961074400}, 
    {     0.00000000667,  4.22974611158,     4539.69249641180}, 
    {     0.00000000793,  5.96535561367,     1457.52593306200}, 
    {     0.00000000565,  0.99421817994,     1894.41906467650}, 
    {     0.00000000578,  2.13199559472,      313.21047591890}, 
    {     0.00000000752,  0.46063700150,      635.23141986800}, 
    {     0.00000000614,  0.15814341318,     1493.09366806600}, 
    {     0.00000000622,  1.98136818407,    25565.32572348040}, 
    {     0.00000000614,  2.48275371627,    25551.09862947879}, 
    {     0.00000000586,  4.17489084697,     2847.52682690940}, 
    {     0.00000000598,  5.29419256363,      565.11568774670}, 
    {     0.00000000616,  2.08837621877,       10.03430830760}, 
    {     0.00000000658,  2.41428707991,      195.13984817330}, 
    {     0.00000000692,  3.13229025530,        7.63481186260}, 
    {     0.00000000569,  3.52605667631,     3067.93946934820}, 
    {     0.00000000525,  3.21922961346,     1098.73880610440}, 
    {     0.00000000685,  4.18539472904,       46.47042291600}, 
    {     0.00000000624,  2.07173693354,      121.25202148330}, 
    {     0.00000000525,  1.47517891985,      446.31134681820}, 
    {     0.00000000508,  2.13584300710,        1.69692102940}, 
    {     0.00000000504,  5.65511769313,     2332.06295581640}, 
    {     0.00000000674,  1.47570122611,     4694.00295470760}, 
    {     0.00000000547,  0.28995741521,      113.38771495710}, 
    {     0.00000000689,  2.98160755722,       11.04570026390}, 
    {     0.00000000546,  4.51208004692,     6275.96230299060}, 
    {     0.00000000561,  1.84479899238,       92.04707395470}, 
    {     0.00000000492,  4.83275232000,     9492.14631500480}, 
    {     0.00000000549,  4.34579166146,     3046.59882834580}, 
    {     0.00000000479,  1.70769710474,     3281.23856478620}, 
    {     0.00000000593,  5.86079640612,      524.06189080210}, 
    {     0.00000000510,  2.62557031270,      529.85102378900}, 
    {     0.00000000480,  0.30754294369,      528.94020556920}, 
    {     0.00000000475,  4.16520247375,     1151.42900414390}, 
    {     0.00000000520,  4.53246652413,      531.17543780290}, 
    {     0.00000000575,  3.53909947579,     1056.93424963440}, 
    {     0.00000000476,  5.35229226962,      560.71045373160}, 
    {     0.00000000470,  4.95335116275,        7.86430652620}, 
    {     0.00000000470,  6.26977555004,     3693.60966166060}, 
    {     0.00000000610,  6.20128372098,     1884.12412393800}, 
    {     0.00000000513,  4.19850316370,     1057.89745748090}, 
    {     0.00000000545,  1.19385752069,     1514.29129671650}, 
    {     0.00000000461,  0.16951411708,    26087.90314157420}, 
    {     0.00000000614,  5.42289673768,     2090.30967237520}, 
    {     0.00000000487,  3.71760211139,      447.93883187840}, 
    {     0.00000000592,  2.91424148255,     8624.21265092720}, 
    {     0.00000000449,  5.24967420622,    10213.28554621100}, 
    {     0.00000000425,  2.71416734228,     1064.04779663520}, 
    {     0.00000000510,  5.81591864532,      529.53090640020}, 
    {     0.00000000520,  3.25538472195,      600.54041039880}, 
    {     0.00000000461,  3.87803707104,     2015.67108615980}, 
    {     0.00000000430,  1.28652623263,      505.31194270640}, 
    {     0.00000000433,  3.43823137684,     1152.17976366930}, 
    {     0.00000000422,  5.12631540623,      944.98282327580}, 
    {     0.00000000410,  1.24248975309,     5069.38346150640}, 
    {     0.00000000411,  2.95117124177,     4326.39340097380}, 
    {     0.00000000419,  5.16120679625,     1173.52040467170}, 
    {     0.00000000412,  2.98125446330,      554.06998748280}, 
    {     0.00000000472,  0.12243647414,      245.54242435240}, 
    {     0.00000000402,  5.88796637322,     1570.91364801910}, 
    {     0.00000000505,  1.49028912471,     3782.47534187760}, 
    {     0.00000000439,  3.06170334768,     1475.68518032670}, 
    {     0.00000000426,  3.12237794195,    12566.15169998280}, 
    {     0.00000000501,  0.09797922397,     1912.57831194120}, 
    {     0.00000000434,  3.59362426939,     3259.89792378380}, 
    {     0.00000000398,  4.91510709622,     4120.20785253660}, 
    {     0.00000000425,  4.74522508051,     1080.72257119160}, 
    {     0.00000000412,  6.26668629942,      512.28247735530}, 
    {     0.00000000377,  5.63771534471,      988.53248488500}, 
    {     0.00000000376,  1.04960792457,        6.36278747540}, 
    {     0.00000000387,  0.82173742289,     2758.66114669240}, 
    {     0.00000000398,  3.16033099794,        1.48447270830}, 
    {     0.00000000392,  1.86519119748,      885.43971066640}, 
};


static const struct ln_vsop jupiter_radius_r2[RADIUS_R2] = {
    {     0.00079644957,  1.35865949884,      529.69096509460}, 
    {     0.00008251645,  5.77774460400,      522.57741809380}, 
    {     0.00007029940,  3.27477392111,      536.80451209540}, 
    {     0.00005314031,  1.83835031247,     1059.38193018920}, 
    {     0.00001861184,  2.97686957956,        7.11354700080}, 
    {     0.00000836256,  4.19892740368,      419.48464387520}, 
    {     0.00000964420,  5.48029587251,      515.46387109300}, 
    {     0.00000406408,  3.78248932836,     1066.49547719000}, 
    {     0.00000426544,  2.22743958182,      639.89728631400}, 
    {     0.00000377334,  2.24232535935,     1589.07289528380}, 
    {     0.00000497914,  3.14159265359,        0.00000000000}, 
    {     0.00000339124,  6.12690872435,      625.67019231240}, 
    {     0.00000362961,  5.36776401268,      206.18554843720}, 
    {     0.00000342139,  6.09909325177,     1052.26838318840}, 
    {     0.00000279940,  4.26158071104,      412.37109687440}, 
    {     0.00000332558,  0.00332561805,      426.59819087600}, 
    {     0.00000229775,  0.70510840437,      735.87651353180}, 
    {     0.00000200884,  3.06805028347,      543.91805909620}, 
    {     0.00000199660,  4.42869041267,      103.09277421860}, 
    {     0.00000257306,  0.96267482500,      632.78373931320}, 
    {     0.00000138577,  2.93153004432,       14.22709400160}, 
    {     0.00000113380,  0.78831018317,      728.76296653100}, 
    {     0.00000085848,  5.14257631438,      323.50541665740}, 
    {     0.00000094695,  1.70378030966,      838.96928775040}, 
    {     0.00000083674,  0.05892269245,      309.27832265580}, 
    {     0.00000075194,  1.60633621497,      956.28915597060}, 
    {     0.00000070197,  1.50916343132,      213.29909543800}, 
    {     0.00000080209,  2.98293613006,      742.99006053260}, 
    {     0.00000056365,  0.95014515126,     1162.47470440780}, 
    {     0.00000061758,  6.10246926546,     1045.15483618760}, 
    {     0.00000066425,  5.47411271821,      199.07200143640}, 
    {     0.00000050128,  2.72034786035,      532.87235883230}, 
    {     0.00000051793,  5.58477632168,      942.06206196900}, 
    {     0.00000039925,  5.94843040319,       95.97922721780}, 
    {     0.00000044584,  5.52437023269,      508.35032409220}, 
    {     0.00000044215,  0.26965913924,      526.50957135690}, 
    {     0.00000030130,  0.93896301926,     1155.36115740700}, 
    {     0.00000028433,  2.87743261296,      525.75881183150}, 
    {     0.00000026377,  4.26907277677,     1596.18644228460}, 
    {     0.00000027064,  2.80927398799,     1169.58825140860}, 
    {     0.00000027531,  2.64852579481,     2118.76386037840}, 
    {     0.00000022695,  0.18097965354,      302.16477565500}, 
    {     0.00000029439,  1.78672212056,      831.85574074960}, 
    {     0.00000020007,  0.03856532918,      949.17560896980}, 
    {     0.00000019915,  1.15792331540,      533.62311835770}, 
    {     0.00000021698,  1.88986950330,     1272.68102562720}, 
    {     0.00000017678,  4.14815218724,      846.08283475120}, 
    {     0.00000017064,  5.88794387217,     1258.45393162560}, 
    {     0.00000021474,  4.34579246643,      316.39186965660}, 
    {     0.00000021174,  0.54776446005,     1265.56747862640}, 
    {     0.00000019878,  0.06616288602,     1581.95934828300}, 
    {     0.00000017028,  0.53404092917,     1368.66025284500}, 
    {     0.00000012874,  3.89924775426,      433.71173787680}, 
    {     0.00000012887,  0.81112211137,      110.20632121940}, 
    {     0.00000011716,  0.40420153376,     1361.54670584420}, 
    {     0.00000011655,  4.43864372476,      405.25754987360}, 
    {     0.00000012042,  2.22601252935,      220.41264243880}, 
    {     0.00000009620,  6.01003863537,      853.19638175200}, 
    {     0.00000010252,  0.99356542172,     1471.75302706360}, 
    {     0.00000009102,  1.61635845262,     1692.16566950240}, 
    {     0.00000008722,  3.51382233353,     1073.60902419080}, 
    {     0.00000008283,  5.61696036887,     1574.84580128220}, 
    {     0.00000008917,  6.26263765188,      519.39602435610}, 
    {     0.00000007962,  0.64245582750,     1478.86657406440}, 
    {     0.00000007722,  0.17138136003,     1685.05212250160}, 
    {     0.00000007445,  0.90537428710,       88.86568021700}, 
    {     0.00000007337,  0.88996282570,      721.64941953020}, 
    {     0.00000009118,  1.51639567636,     1148.24761040620}, 
    {     0.00000006139,  2.49651421842,        3.18139373770}, 
    {     0.00000007001,  4.44209624915,      330.61896365820}, 
    {     0.00000005235,  2.79243270986,       21.34064100240}, 
    {     0.00000005041,  2.97840393432,     1375.77379984580}, 
    {     0.00000004937,  0.04442899397,     1677.93857550080}, 
    {     0.00000004633,  2.26661974645,     1485.98012106520}, 
    {     0.00000004667,  0.84935842035,        3.93215326310}, 
    {     0.00000005341,  0.86294969395,     1788.14489672020}, 
    {     0.00000004248,  0.41663016954,      629.60234557550}, 
    {     0.00000004187,  1.62198715560,      635.96513305090}, 
    {     0.00000003629,  2.71174024514,      551.03160609700}, 
    {     0.00000004453,  1.27731121245,     1464.63948006280}, 
    {     0.00000003266,  0.54602174256,     1795.25844372100}, 
    {     0.00000003409,  1.20638860556,     1905.46476494040}, 
    {     0.00000003164,  6.20189662302,     1038.04128918680}, 
    {     0.00000003096,  6.21099164255,     2001.44399215820}, 
    {     0.00000003404,  2.44670518809,      539.98590583310}, 
    {     0.00000003168,  5.58075929197,      191.95845443560}, 
    {     0.00000002201,  5.33344494715,     1891.23767093880}, 
    {     0.00000002553,  3.20949626593,     1062.56332392690}, 
    {     0.00000002386,  4.29199230828,      963.40270297140}, 
    {     0.00000002597,  0.57986674442,     2104.53676637680}, 
    {     0.00000002547,  0.14627545776,      750.10360753340}, 
    {     0.00000002609,  4.82665360488,      416.30325013750}, 
    {     0.00000002187,  1.71707514653,      628.85158605010}, 
    {     0.00000002258,  6.17429279705,     1994.33044515740}, 
    {     0.00000002624,  2.36922205485,      227.52618943960}, 
    {     0.00000002097,  3.31460321409,     1699.27921650320}, 
    {     0.00000002027,  3.15533834136,      611.44309831080}, 
    {     0.00000002081,  0.31057710726,     2111.65031337760}, 
    {     0.00000002484,  0.04731413707,     1898.35121793960}, 
    {     0.00000001963,  0.29583638556,      636.71589257630}, 
    {     0.00000002279,  1.96058124545,      824.74219374880}, 
    {     0.00000001829,  4.69907372627,     2125.87740737920}, 
    {     0.00000001829,  0.33004933298,      295.05122865420}, 
    {     0.00000002553,  1.24739305569,     2221.85663459700}, 
    {     0.00000001785,  3.51009274020,      647.01083331480}, 
    {     0.00000001786,  3.46994340828,     1055.44977692610}, 
    {     0.00000001742,  2.43853510157,       10.29494073850}, 
    {     0.00000001850,  1.60578508516,     2008.55753915900}, 
    {     0.00000001971,  1.15435477931,      618.55664531160}, 
    {     0.00000001611,  5.83466560322,      422.66603761290}, 
    {     0.00000001639,  0.45469643466,     1056.20053645150}, 
    {     0.00000001628,  5.86754764931,     2317.83586181480}, 
    {     0.00000002099,  1.05944599014,     1781.03134971940}, 
    {     0.00000001570,  2.39516560987,      440.82528487760}, 
    {     0.00000001999,  4.62828691526,      423.41679713830}, 
    {     0.00000001480,  0.02394813605,     1382.88734684660}, 
    {     0.00000001502,  5.74598263477,      117.31986822020}, 
    {     0.00000001881,  2.76425929784,     1802.37199072180}, 
    {     0.00000001983,  2.99080832362,     2648.45482547300}, 
    {     0.00000001402,  0.15904673895,     2420.92863603340}, 
    {     0.00000001174,  1.55354182426,      380.12776796000}, 
    {     0.00000001321,  1.26221998203,     1063.31408345230}, 
    {     0.00000001150,  4.12219328847,      547.85021235930}, 
    {     0.00000001080,  4.41192013439,      934.94851496820}, 
    {     0.00000001138,  5.93242605811,     2310.72231481400}, 
    {     0.00000001033,  5.63854408052,       99.91138048090}, 
    {     0.00000000949,  6.07298626146,      511.53171782990}, 
    {     0.00000001012,  3.80744305824,     1603.29998928540}, 
    {     0.00000000922,  6.16494528393,      945.99421523210}, 
    {     0.00000000915,  5.22425774632,     2207.62954059540}, 
    {     0.00000000860,  2.48740591818,     6283.07584999140}, 
    {     0.00000000836,  1.08651799806,       81.75213321620}, 
    {     0.00000001165,  0.72510519647,     2097.42321937600}, 
    {     0.00000000851,  4.69371733745,     5746.27133789600}, 
    {     0.00000000789,  3.91035208173,    10213.28554621100}, 
    {     0.00000000846,  0.77030801324,     5760.49843189760}, 
    {     0.00000000924,  1.43423249860,      732.69511979410}, 
    {     0.00000000805,  6.11630827296,     9676.48103411560}, 
    {     0.00000000800,  2.19289534160,     9690.70812811720}, 
    {     0.00000000812,  5.00490295474,      319.57326339430}, 
    {     0.00000000841,  1.22483116811,      952.35700270750}, 
    {     0.00000000720,  3.95975713584,      337.73251065900}, 
    {     0.00000000711,  1.23970970528,      106.27416795630}, 
    {     0.00000000889,  0.10251260092,     2737.32050569000}, 
    {     0.00000000858,  1.51763095265,     2324.94940881560}, 
    {     0.00000000868,  2.67598866406,     3370.10424500320}, 
    {     0.00000000710,  0.65180853077,     2538.24850425360}, 
    {     0.00000000743,  0.60536479474,     1354.43315884340}, 
    {     0.00000000633,  1.37719198152,      124.43341522100}, 
    {     0.00000000866,  3.02831268213,     3046.59882834580}, 
    {     0.00000000733,  5.84583969196,     2634.22773147140}, 
    {     0.00000000691,  1.14062641255,     2641.34127847220}, 
    {     0.00000000593,  1.80277592426,      453.42489381900}, 
    {     0.00000000660,  6.01207640959,     1049.08698945070}, 
    {     0.00000000771,  6.01059588645,     2214.74308759620}, 
    {     0.00000000586,  5.68149019460,      107.02492748170}, 
    {     0.00000000639,  4.77149952374,      860.30992875280}, 
    {     0.00000000782,  2.52401202862,     3679.38256765900}, 
    {     0.00000000631,  2.27765412816,     2015.67108615980}, 
    {     0.00000000779,  2.38608991574,     3267.01147078460}, 
    {     0.00000000584,  3.00542907219,     1262.38608488870}, 
    {     0.00000000543,  3.09924086245,     3281.23856478620}, 
    {     0.00000000535,  2.42171003067,      739.05790726950}, 
    {     0.00000000681,  1.18831331541,      739.80866679490}, 
    {     0.00000000621,  1.24462887440,     3803.81598288000}, 
    {     0.00000000717,  4.14222389339,     9683.59458111640}, 
    {     0.00000000546,  3.43095520503,       18.15924726470}, 
    {     0.00000000545,  5.65426574985,     2627.11418447060}, 
    {     0.00000000538,  4.92334194042,      447.79581952650}, 
    {     0.00000000534,  0.99911551571,      462.02291352810}, 
    {     0.00000000541,  6.19275150397,     1987.21689815660}, 
    {     0.00000000511,  3.28553278370,        4.66586644600}, 
    {     0.00000000537,  5.33205206604,     2751.54759969160}, 
    {     0.00000000651,  5.12199308959,     3156.80514956520}, 
    {     0.00000000510,  5.35664230912,        9.56122755560}, 
    {     0.00000000544,  1.81488805078,     1251.34038462480}, 
    {     0.00000000426,  2.10841334313,      149.56319713460}, 
    {     0.00000000516,  3.89424540015,     2516.90786325120}, 
    {     0.00000000543,  5.56620814561,     2524.02141025200}, 
    {     0.00000000519,  2.43126348834,     3686.49611465980}, 
    {     0.00000000404,  2.77840802846,        7.16173111060}, 
    {     0.00000000533,  4.77083438961,     3473.19701922180}, 
    {     0.00000000386,  6.06244501785,      203.00415469950}, 
    {     0.00000000482,  0.38718011166,     2428.04218303420}, 
    {     0.00000000434,  5.36713537673,     2531.13495725280}, 
    {     0.00000000370,  6.04174787347,     1670.82502850000}, 
};


static const struct ln_vsop jupiter_radius_r3[RADIUS_R3] = {
    {     0.00003519277,  6.05800355513,      529.69096509460}, 
    {     0.00001073281,  1.67319166156,      536.80451209540}, 
    {     0.00000915630,  1.41326157617,      522.57741809380}, 
    {     0.00000341654,  0.52294532787,     1059.38193018920}, 
    {     0.00000254881,  1.19631092831,        7.11354700080}, 
    {     0.00000221477,  0.95234304351,      515.46387109300}, 
    {     0.00000069020,  2.26889455907,     1066.49547719000}, 
    {     0.00000089777,  3.14159265359,        0.00000000000}, 
    {     0.00000057885,  1.41227055539,      543.91805909620}, 
    {     0.00000057700,  0.52564805704,      639.89728631400}, 
    {     0.00000051213,  5.97994255422,      412.37109687440}, 
    {     0.00000046968,  1.57861666908,      625.67019231240}, 
    {     0.00000042744,  6.11814173992,      419.48464387520}, 
    {     0.00000037444,  1.18048940249,       14.22709400160}, 
    {     0.00000033816,  1.66573652907,     1052.26838318840}, 
    {     0.00000031166,  1.04468072620,     1589.07289528380}, 
    {     0.00000029943,  4.63498871771,      426.59819087600}, 
    {     0.00000033558,  0.84853879170,      206.18554843720}, 
    {     0.00000020709,  2.50340319894,      728.76296653100}, 
    {     0.00000014470,  0.96111460506,      508.35032409220}, 
    {     0.00000012974,  1.50391478213,     1045.15483618760}, 
    {     0.00000011596,  3.55299164531,      323.50541665740}, 
    {     0.00000012357,  2.60797398650,      735.87651353180}, 
    {     0.00000015065,  0.87961214090,      199.07200143640}, 
    {     0.00000011062,  1.78854133467,      309.27832265580}, 
    {     0.00000010576,  0.00265970762,      956.28915597060}, 
    {     0.00000009798,  6.24533081819,      103.09277421860}, 
    {     0.00000006725,  1.86312777034,      302.16477565500}, 
    {     0.00000009133,  3.46071465629,      838.96928775040}, 
    {     0.00000007338,  1.28438797074,      742.99006053260}, 
    {     0.00000007182,  0.91717952341,      942.06206196900}, 
    {     0.00000005482,  1.35541254124,       95.97922721780}, 
    {     0.00000006754,  3.45186268696,      831.85574074960}, 
    {     0.00000004626,  2.83572146596,     1596.18644228460}, 
    {     0.00000004106,  6.01730779864,      213.29909543800}, 
    {     0.00000003942,  1.19384143223,     1169.58825140860}, 
    {     0.00000003469,  6.10664206989,      405.25754987360}, 
    {     0.00000002861,  2.32367020387,     1155.36115740700}, 
    {     0.00000002519,  0.42500820125,      220.41264243880}, 
    {     0.00000002468,  1.84219414782,      532.87235883230}, 
    {     0.00000002322,  1.57653167974,     2118.76386037840}, 
    {     0.00000002283,  0.13415259559,      632.78373931320}, 
    {     0.00000002243,  1.91751229130,     1073.60902419080}, 
    {     0.00000002285,  5.94194291108,     1162.47470440780}, 
    {     0.00000002137,  1.06953434212,       21.34064100240}, 
    {     0.00000002515,  0.33520672477,     1272.68102562720}, 
    {     0.00000002042,  5.92779916530,      110.20632121940}, 
    {     0.00000001927,  2.58542297225,       88.86568021700}, 
    {     0.00000002021,  2.21761113830,      433.71173787680}, 
    {     0.00000001943,  1.46376661665,     1258.45393162560}, 
    {     0.00000001700,  1.88459425041,      525.75881183150}, 
    {     0.00000001815,  2.67626558650,      330.61896365820}, 
    {     0.00000001821,  2.75572507789,      721.64941953020}, 
    {     0.00000002068,  3.17049523925,     1148.24761040620}, 
    {     0.00000001866,  2.28678298902,     1361.54670584420}, 
    {     0.00000001526,  4.47646904898,      853.19638175200}, 
    {     0.00000001508,  0.11633951449,      949.17560896980}, 
    {     0.00000001655,  0.44340210808,      533.62311835770}, 
    {     0.00000001572,  0.45863923926,      526.50957135690}, 
    {     0.00000001161,  3.10471097791,      963.40270297140}, 
    {     0.00000001162,  1.19270352887,     1574.84580128220}, 
    {     0.00000001140,  2.46324106660,      846.08283475120}, 
    {     0.00000001259,  1.24988357144,     1038.04128918680}, 
    {     0.00000001396,  0.69581007586,      551.03160609700}, 
    {     0.00000001182,  1.93125671013,     1581.95934828300}, 
    {     0.00000000894,  2.85762385272,      519.39602435610}, 
    {     0.00000000983,  4.17198081351,     2627.11418447060}, 
    {     0.00000001061,  0.66716890315,      539.98590583310}, 
    {     0.00000000859,  4.91931457958,      611.44309831080}, 
    {     0.00000000918,  4.89690742057,     1670.82502850000}, 
    {     0.00000000866,  3.00153408458,     1368.66025284500}, 
    {     0.00000001115,  0.97017156126,      227.52618943960}, 
    {     0.00000000887,  3.68665606145,      824.74219374880}, 
    {     0.00000000737,  3.20041743453,     2125.87740737920}, 
    {     0.00000000730,  2.32845485663,     2317.83586181480}, 
    {     0.00000000828,  1.01037712742,      191.95845443560}, 
    {     0.00000000778,  0.25303611679,     1141.13406340540}, 
    {     0.00000000757,  2.24232615954,     2538.24850425360}, 
    {     0.00000000720,  0.55787809007,      440.82528487760}, 
    {     0.00000000672,  4.17028096565,     1692.16566950240}, 
    {     0.00000000691,  5.78026436421,     1485.98012106520}, 
    {     0.00000000611,  2.66934999696,     1265.56747862640}, 
    {     0.00000000592,  2.26781665598,     1471.75302706360}, 
    {     0.00000000561,  6.11300561068,     1279.79457262800}, 
    {     0.00000000566,  1.93294355027,     2634.22773147140}, 
    {     0.00000000545,  2.21244108948,     1062.56332392690}, 
    {     0.00000000640,  2.47352731748,     1699.27921650320}, 
    {     0.00000000694,  4.71564977334,      750.10360753340}, 
    {     0.00000000604,  1.97421641416,     1677.93857550080}, 
    {     0.00000000501,  2.45269887786,       81.75213321620}, 
    {     0.00000000552,  4.37775459043,     1382.88734684660}, 
    {     0.00000000556,  5.31872445991,     2413.81508903260}, 
    {     0.00000000589,  0.19759573714,       10.29494073850}, 
    {     0.00000000497,  2.52744546318,     2207.62954059540}, 
    {     0.00000000416,  6.19072120624,      934.94851496820}, 
    {     0.00000000433,  5.80559659477,     1478.86657406440}, 
    {     0.00000000395,  2.34556406839,      295.05122865420}, 
};


static const struct ln_vsop jupiter_radius_r4[RADIUS_R4] = {
    {     0.00000128623,  0.08347608895,      536.80451209540}, 
    {     0.00000113458,  4.24818938180,      529.69096509460}, 
    {     0.00000082704,  3.29801136583,      522.57741809380}, 
    {     0.00000037897,  2.73402665560,      515.46387109300}, 
    {     0.00000026713,  5.68996992467,        7.11354700080}, 
    {     0.00000017808,  5.40366594364,     1059.38193018920}, 
    {     0.00000012564,  6.00543529469,      543.91805909620}, 
    {     0.00000009272,  0.75619260404,     1066.49547719000}, 
    {     0.00000008141,  5.68230705037,       14.22709400160}, 
    {     0.00000006174,  5.10190413726,      639.89728631400}, 
    {     0.00000006920,  1.42214334807,      412.37109687440}, 
    {     0.00000005327,  3.33829390777,      625.67019231240}, 
    {     0.00000002895,  3.38407751603,     1052.26838318840}, 
    {     0.00000002696,  4.18310762577,      728.76296653100}, 
    {     0.00000002435,  2.96139551556,      426.59819087600}, 
    {     0.00000002176,  6.21232313303,     1589.07289528380}, 
    {     0.00000002008,  3.13891134942,     1045.15483618760}, 
    {     0.00000001817,  2.74670205576,      206.18554843720}, 
    {     0.00000001883,  1.87835568033,      419.48464387520}, 
    {     0.00000001501,  1.26929907808,     1596.18644228460}, 
    {     0.00000001701,  2.58901479440,      199.07200143640}, 
    {     0.00000001689,  0.00000000000,        0.00000000000}, 
    {     0.00000001148,  5.18914327333,      831.85574074960}, 
    {     0.00000001033,  5.35702238710,      220.41264243880}, 
    {     0.00000000874,  5.79483644819,     1169.58825140860}, 
    {     0.00000000854,  4.55476058022,      956.28915597060}, 
    {     0.00000000913,  1.89622509837,     1148.24761040620}, 
    {     0.00000000949,  0.68597092334,     1361.54670584420}, 
    {     0.00000000788,  1.44319075028,     1272.68102562720}, 
    {     0.00000000774,  3.21426219962,      508.35032409220}, 
    {     0.00000000921,  5.33422516215,      551.03160609700}, 
    {     0.00000000681,  0.44800059149,     1073.60902419080}, 
    {     0.00000000681,  5.21435913114,       21.34064100240}, 
    {     0.00000000587,  4.57539103016,      110.20632121940}, 
    {     0.00000000578,  1.97098995055,      647.01083331480}, 
    {     0.00000000596,  2.85043907413,      191.95845443560}, 
    {     0.00000000599,  2.43146933611,      117.31986822020}, 
    {     0.00000000544,  0.53039419311,      330.61896365820}, 
    {     0.00000000545,  3.50461220615,      302.16477565500}, 
    {     0.00000000538,  4.22160404735,       88.86568021700}, 
    {     0.00000000757,  2.28818475655,      942.06206196900}, 
    {     0.00000000562,  1.48594378600,        3.18139373770}, 
    {     0.00000000631,  1.83863158533,       10.29494073850}, 
    {     0.00000000504,  2.08322743695,      103.09277421860}, 
    {     0.00000000462,  0.40130574859,      433.71173787680}, 
};


static const struct ln_vsop jupiter_radius_r5[RADIUS_R5] = {
    {     0.00000011193,  4.74280611863,      536.80451209540}, 
    {     0.00000004288,  5.90497787277,      522.57741809380}, 
    {     0.00000002004,  3.65178377123,        7.11354700080}, 
    {     0.00000002118,  5.57290745004,      515.46387109300}, 
    {     0.00000001908,  4.29659647286,      543.91805909620}, 
    {     0.00000001534,  5.46373729640,     1066.49547719000}, 
    {     0.00000001596,  4.11045079899,     1059.38193018920}, 
    {     0.00000001301,  3.72955393027,       14.22709400160}, 
    {     0.00000001033,  4.50671820436,      529.69096509460}, 
};

/*! \fn void ln_get_jupiter_equ_coords (double JD, struct ln_equ_posn * position);
* \param JD julian Day
* \param position Pointer to store position
*
* Calculates Jupiter's equatorial position for given julian day.
* This function includes calculations for planetary aberration and refers
* to the FK5 reference frame.
*
* To get the complete equatorial coordinates, corrections for nutation
* have to be applied.
*
* The position returned is accurate to within 0.1 arcsecs.
*/ 
void ln_get_jupiter_equ_coords (double JD, struct ln_equ_posn * position)
{
	struct ln_helio_posn h_sol, h_jupiter;
	struct ln_rect_posn g_sol, g_jupiter;
	double a,b,c;
	double ra, dec, delta, diff, last, t = 0;
	
	/* need typdef for solar heliocentric coords */
	ln_get_solar_geom_coords (JD, &h_sol);
	ln_get_rect_from_helio (&h_sol,  &g_sol);
	
	do {
		last = t;
		ln_get_jupiter_helio_coords (JD - t, &h_jupiter);
		ln_get_rect_from_helio (&h_jupiter, &g_jupiter);

		/* equ 33.10 pg 229 */
		a = g_sol.X + g_jupiter.X;
		b = g_sol.Y + g_jupiter.Y;
		c = g_sol.Z + g_jupiter.Z;
	
		delta = a*a + b*b + c*c;
		delta = sqrt (delta);
		t = delta * 0.0057755183;
		diff = t - last;
	} while (diff > 0.0001 || diff < -0.0001);
		
	ra = atan2 (b,a);
	dec = c / delta;
	dec = asin (dec);

	/* back to hours, degrees */
	position->ra = ln_range_degrees(ln_rad_to_deg (ra));
	position->dec = ln_rad_to_deg (dec);
}
	
/*! \fn void ln_get_jupiter_helio_coords (double JD, struct ln_helio_posn * position)
* \param JD Julian Day
* \param position Pointer to store heliocentric position
*
* Calculate Jupiters heliocentric (refered to the centre of the Sun) coordinates
* in the FK5 reference frame for the given julian day.
* Longitude and Latitude are in degrees, whilst radius vector is in AU.
*/
/* Chapter 31 Pg 206-207 Equ 31.1 31.2 , 31.3 using VSOP 87 
*/
void ln_get_jupiter_helio_coords (double JD, struct ln_helio_posn * position)
{
	double t, t2, t3, t4, t5;
	double L0, L1, L2, L3, L4, L5;
	double B0, B1, B2, B3, B4, B5;
	double R0, R1, R2, R3, R4, R5;
           	
	/* check cache first */
	if (JD == cJD) {
		/* cache hit */
		position->L = cL;
		position->B = cB;
		position->R = cR;
		return;
	}
	
	/* get julian ephemeris day */
	t = (JD - 2451545.0) / 365250;
	t2 = t * t;
	t3 = t2 * t;
	t4 = t3 * t;
	t5 = t4 * t;
	
	/* calc L series */
	L0 = ln_calc_series (jupiter_longitude_l0, LONG_L0, t);
	L1 = ln_calc_series (jupiter_longitude_l1, LONG_L1, t);
	L2 = ln_calc_series (jupiter_longitude_l2, LONG_L2, t);
	L3 = ln_calc_series (jupiter_longitude_l3, LONG_L3, t);
	L4 = ln_calc_series (jupiter_longitude_l4, LONG_L4, t);
	L5 = ln_calc_series (jupiter_longitude_l5, LONG_L5, t);
	position->L = (L0 + L1 * t + L2 * t2 + L3 * t3 + L4 * t4 + L5 * t5);

	/* calc B series */
	B0 = ln_calc_series (jupiter_latitude_b0, LAT_B0, t);
	B1 = ln_calc_series (jupiter_latitude_b1, LAT_B1, t);
	B2 = ln_calc_series (jupiter_latitude_b2, LAT_B2, t);
	B3 = ln_calc_series (jupiter_latitude_b3, LAT_B3, t);
	B4 = ln_calc_series (jupiter_latitude_b4, LAT_B4, t);
	B5 = ln_calc_series (jupiter_latitude_b5, LAT_B5, t);
	position->B = (B0 + B1 * t + B2 * t2 + B3 * t3 + B4 * t4 + B5 * t5);


	/* calc R series */
	R0 = ln_calc_series (jupiter_radius_r0, RADIUS_R0, t);
	R1 = ln_calc_series (jupiter_radius_r1, RADIUS_R1, t);
	R2 = ln_calc_series (jupiter_radius_r2, RADIUS_R2, t);
	R3 = ln_calc_series (jupiter_radius_r3, RADIUS_R3, t);
	R4 = ln_calc_series (jupiter_radius_r4, RADIUS_R4, t);
	R5 = ln_calc_series (jupiter_radius_r5, RADIUS_R5, t);
	position->R = (R0 + R1 * t + R2 * t2 + R3 * t3 + R4 * t4 + R5 * t5);
	
	/* change to degrees in correct quadrant */
	position->L = ln_rad_to_deg(position->L);
	position->B = ln_rad_to_deg(position->B);
	position->L = ln_range_degrees(position->L);
	
	/* change to fk5 reference frame */
	ln_vsop87_to_fk5 (position, JD);
	
	/* save cache */
	cJD = JD;
	cL = position->L;
	cB = position->B;
	cR = position->R;
}

/*! \fn double ln_get_jupiter_earth_dist (double JD);
* \param JD Julian day.
* \brief Calculate the distance between Jupiter and the Earth in AU
* \return Distance in AU.
*
* Calculates the distance in AU between the Earth and Jupiter for the given julian day.
*/
double ln_get_jupiter_earth_dist (double JD)
{
	struct ln_helio_posn  h_jupiter, h_earth;
	struct ln_rect_posn g_jupiter, g_earth;
	double x, y, z;
	
	/* get heliocentric positions */
	ln_get_jupiter_helio_coords (JD, &h_jupiter);
	ln_get_earth_helio_coords (JD, &h_earth);
	
	/* get geocentric coords */
	ln_get_rect_from_helio (&h_jupiter, &g_jupiter);
	ln_get_rect_from_helio (&h_earth, &g_earth);
	
	/* use pythag */
	x = g_jupiter.X - g_earth.X;
	y = g_jupiter.Y - g_earth.Y;
	z = g_jupiter.Z - g_earth.Z;;
	x = x * x;
	y = y * y;
	z = z * z;

	return sqrt (x + y + z);
}
	
/*! \fn double ln_get_jupiter_solar_dist (double JD);
* \param JD Julian day.
* \brief Calculate the distance between Jupiter and the Sun in AU
* \return Distance in AU.
*
* Calculates the distance in AU between the Sun and Jupiter for the given julian day.
*/ 
double ln_get_jupiter_solar_dist (double JD)
{
	struct ln_helio_posn h_jupiter;
	
	/* get heliocentric position */
	ln_get_jupiter_helio_coords (JD, &h_jupiter);
	return h_jupiter.R;
}
	
/*! \fn double ln_get_jupiter_magnitude (double JD);
* \param JD Julian day
* \brief Calculate the visible magnitude of Jupiter
* \return Visible magnitude of Jupiter
*
* Calculate the visible magnitude of jupiter for the given julian day.
*/ 
double ln_get_jupiter_magnitude (double JD)
{
	double delta, r, i;
	
	/* get distances */
	r = ln_get_jupiter_solar_dist (JD);
	delta = ln_get_jupiter_earth_dist (JD);
	
	/* get phase */
	i = ln_get_jupiter_phase (JD);

	return -9.40 + 5 * log10 (r * delta) + 0.005 * i;
}

/*! \fn double ln_get_jupiter_disk (double JD);
* \param JD Julian day.
* \brief Calculate the illuminated fraction of Jupiter's disk
* \return Illuminated fraction of Jupiters disk (Value between 0 and 1)
*
* Calculate the illuminated fraction of Jupiter's disk for the given Julian
* day.
*/ 
/* Chapter 41 */
double ln_get_jupiter_disk (double JD)
{
	double r,delta,R;	
	
	/* get distances */
	R = ln_get_earth_solar_dist (JD);
	r = ln_get_jupiter_solar_dist (JD);
	delta = ln_get_jupiter_earth_dist (JD);
	
	/* calc fraction angle */
	return (((r + delta) * (r + delta)) - R * R) / (4 * r * delta);
}

/*! \fn double ln_get_jupiter_phase (double JD);
* \param JD Julian Day
* \return Phase angle of Jupiter (degrees)
*
* Calculates the phase angle of Jupiter, that is, the angle Sun -
* Jupiter - Earth for the given Julian day.
*/ 
/* Chapter 41 */
double ln_get_jupiter_phase (double JD)
{
	double i,r,delta,R;	
	
	/* get distances */
	R = ln_get_earth_solar_dist (JD);
	r = ln_get_jupiter_solar_dist (JD);
	delta = ln_get_jupiter_earth_dist (JD);

	/* calc phase */
	i = (r * r + delta * delta - R * R) / (2 * r * delta);
	i = acos (i);
	return ln_rad_to_deg (i);
}


/*! \fn double ln_get_jupiter_rst (double JD, struct ln_lnlat_posn * observer, struct ln_rst_time * rst);
* \param JD Julian day
* \param observer Observers position
* \param rst Pointer to store Rise, Set and Transit time in JD
* \return 0 for success, else 1 for circumpolar.
*
* Calculate the time the rise, set and transit (crosses the local meridian at upper culmination)
* time of Jupiter for the given Julian day.
*
* Note: this functions returns 1 if Jupiter is circumpolar, that is it remains the whole
* day either above or below the horizon.
*/
int ln_get_jupiter_rst (double JD, struct ln_lnlat_posn * observer, struct ln_rst_time * rst)
{
	return ln_get_body_rst_horizon (JD, observer, ln_get_jupiter_equ_coords, LN_STAR_STANDART_HORIZON, rst);
}


/*! \fn double ln_get_jupiter_equ_sdiam (double JD)
* \param JD Julian day
* \return Semidiameter in arc seconds
*
* Calculate the equatorial semidiameter of Jupiter in arc seconds for the 
* given julian day.
*/
double ln_get_jupiter_equ_sdiam (double JD)
{
	double So = 98.44; /* at 1 AU */
	double dist;
	
	dist = ln_get_jupiter_earth_dist (JD);
	return So / dist;
}

/*! \fn double ln_get_jupiter_pol_sdiam (double JD)
* \param JD Julian day
* \return Semidiameter in arc seconds
* \todo Use Jupitercentric latitude of Earth Pg 390
*
* Calculate the polar semidiameter of Jupiter in arc seconds for the 
* given julian day.
*/
double ln_get_jupiter_pol_sdiam (double JD)
{
	double So = 92.06; /* at 1 AU */
	double dist;
	
	dist = ln_get_jupiter_earth_dist (JD);
	return So / dist;
}

/*! \fn void ln_get_jupiter_rect_helio (double JD, struct ln_rect_posn * position)
* \param JD Julian day.
* \param position ointer to return position
*
* Calculate Jupiters rectangular heliocentric coordinates for the
* given Julian day. Coordinates are in AU.
*/
void ln_get_jupiter_rect_helio (double JD, struct ln_rect_posn * position)
{
	struct ln_helio_posn jupiter;
		
	ln_get_jupiter_helio_coords (JD, &jupiter);
	ln_get_rect_from_helio (&jupiter, position);
}
